Solve using the Square Root Property square root of 5x-12- square root of x-3=-1

Math
5x-12-x-3=-1
Move all terms not containing 5x-12 to the right side of the equation.
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Add x to both sides of the equation.
5x-12-3=-1+x
Add 3 to both sides of the equation.
5x-12=-1+x+3
Add -1 and 3.
5x-12=x+2
5x-12=x+2
To remove the radical on the left side of the equation, square both sides of the equation.
5x-122=(x+2)2
Simplify each side of the equation.
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Multiply the exponents in ((5x-12)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(5x-12)12⋅2=(x+2)2
Cancel the common factor of 2.
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Cancel the common factor.
(5x-12)12⋅2=(x+2)2
Rewrite the expression.
(5x-12)1=(x+2)2
(5x-12)1=(x+2)2
(5x-12)1=(x+2)2
Simplify.
5x-12=(x+2)2
5x-12=(x+2)2
Solve for x.
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Simplify (x+2)2.
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Rewrite (x+2)2 as (x+2)(x+2).
5x-12=(x+2)(x+2)
Expand (x+2)(x+2) using the FOIL Method.
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Apply the distributive property.
5x-12=x(x+2)+2(x+2)
Apply the distributive property.
5x-12=xx+x⋅2+2(x+2)
Apply the distributive property.
5x-12=xx+x⋅2+2x+2⋅2
5x-12=xx+x⋅2+2x+2⋅2
Simplify and combine like terms.
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Simplify each term.
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Multiply xx.
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Raise x to the power of 1.
5x-12=x1x+x⋅2+2x+2⋅2
Raise x to the power of 1.
5x-12=x1x1+x⋅2+2x+2⋅2
Use the power rule aman=am+n to combine exponents.
5x-12=x1+1+x⋅2+2x+2⋅2
Add 1 and 1.
5x-12=x2+x⋅2+2x+2⋅2
5x-12=x2+x⋅2+2x+2⋅2
Rewrite x2 as x.
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Use axn=axn to rewrite x as x12.
5x-12=(x12)2+x⋅2+2x+2⋅2
Apply the power rule and multiply exponents, (am)n=amn.
5x-12=x12⋅2+x⋅2+2x+2⋅2
Combine 12 and 2.
5x-12=x22+x⋅2+2x+2⋅2
Cancel the common factor of 2.
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Cancel the common factor.
5x-12=x22+x⋅2+2x+2⋅2
Divide 1 by 1.
5x-12=x1+x⋅2+2x+2⋅2
5x-12=x1+x⋅2+2x+2⋅2
Simplify.
5x-12=x+x⋅2+2x+2⋅2
5x-12=x+x⋅2+2x+2⋅2
Move 2 to the left of x.
5x-12=x+2⋅x+2x+2⋅2
Multiply 2 by 2.
5x-12=x+2x+2x+4
5x-12=x+2x+2x+4
Add 2x and 2x.
5x-12=x+4x+4
5x-12=x+4x+4
5x-12=x+4x+4
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
x+4x+4=5x-12
Move all terms not containing x to the right side of the equation.
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Subtract x from both sides of the equation.
4x+4=5x-12-x
Subtract 4 from both sides of the equation.
4x=5x-12-x-4
Subtract x from 5x.
4x=4x-12-4
Subtract 4 from -12.
4x=4x-16
4x=4x-16
Divide each term by 4 and simplify.
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Divide each term in 4x=4x-16 by 4.
4×4=4×4+-164
Cancel the common factor of 4.
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Cancel the common factor.
4×4=4×4+-164
Divide x by 1.
x=4×4+-164
x=4×4+-164
Simplify each term.
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Cancel the common factor of 4.
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Cancel the common factor.
x=4×4+-164
Divide x by 1.
x=x+-164
x=x+-164
Divide -16 by 4.
x=x-4
x=x-4
x=x-4
To remove the radical on the left side of the equation, square both sides of the equation.
x2=(x-4)2
Simplify each side of the equation.
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Multiply the exponents in (x12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
x12⋅2=(x-4)2
Cancel the common factor of 2.
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Cancel the common factor.
x12⋅2=(x-4)2
Rewrite the expression.
x1=(x-4)2
x1=(x-4)2
x1=(x-4)2
Simplify.
x=(x-4)2
x=(x-4)2
Solve for x.
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Simplify (x-4)2.
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Rewrite (x-4)2 as (x-4)(x-4).
x=(x-4)(x-4)
Expand (x-4)(x-4) using the FOIL Method.
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Apply the distributive property.
x=x(x-4)-4(x-4)
Apply the distributive property.
x=x⋅x+x⋅-4-4(x-4)
Apply the distributive property.
x=x⋅x+x⋅-4-4x-4⋅-4
x=x⋅x+x⋅-4-4x-4⋅-4
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
x=x2+x⋅-4-4x-4⋅-4
Move -4 to the left of x.
x=x2-4⋅x-4x-4⋅-4
Multiply -4 by -4.
x=x2-4x-4x+16
x=x2-4x-4x+16
Subtract 4x from -4x.
x=x2-8x+16
x=x2-8x+16
x=x2-8x+16
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
x2-8x+16=x
Move all terms containing x to the left side of the equation.
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Subtract x from both sides of the equation.
x2-8x+16-x=0
Subtract x from -8x.
x2-9x+16=0
x2-9x+16=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-9, and c=16 into the quadratic formula and solve for x.
9±(-9)2-4⋅(1⋅16)2⋅1
Simplify.
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Simplify the numerator.
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Raise -9 to the power of 2.
x=9±81-4⋅(1⋅16)2⋅1
Multiply 16 by 1.
x=9±81-4⋅162⋅1
Multiply -4 by 16.
x=9±81-642⋅1
Subtract 64 from 81.
x=9±172⋅1
x=9±172⋅1
Multiply 2 by 1.
x=9±172
x=9±172
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -9 to the power of 2.
x=9±81-4⋅(1⋅16)2⋅1
Multiply 16 by 1.
x=9±81-4⋅162⋅1
Multiply -4 by 16.
x=9±81-642⋅1
Subtract 64 from 81.
x=9±172⋅1
x=9±172⋅1
Multiply 2 by 1.
x=9±172
Change the ± to +.
x=9+172
x=9+172
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -9 to the power of 2.
x=9±81-4⋅(1⋅16)2⋅1
Multiply 16 by 1.
x=9±81-4⋅162⋅1
Multiply -4 by 16.
x=9±81-642⋅1
Subtract 64 from 81.
x=9±172⋅1
x=9±172⋅1
Multiply 2 by 1.
x=9±172
Change the ± to -.
x=9-172
x=9-172
The final answer is the combination of both solutions.
x=9+172,9-172
x=9+172,9-172
x=9+172,9-172
Exclude the solutions that do not make 5x-12-x-3=-1 true.
x=9+172
The result can be shown in multiple forms.
Exact Form:
x=9+172
Decimal Form:
x=6.56155281…
Solve using the Square Root Property square root of 5x-12- square root of x-3=-1

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