Solve for x square root of 3x+28=1+ square root of x+9

Math
3x+28=1+x+9
To remove the radical on the left side of the equation, square both sides of the equation.
3x+282=(1+x+9)2
Simplify each side of the equation.
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Multiply the exponents in ((3x+28)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(3x+28)12⋅2=(1+x+9)2
Cancel the common factor of 2.
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Cancel the common factor.
(3x+28)12⋅2=(1+x+9)2
Rewrite the expression.
(3x+28)1=(1+x+9)2
(3x+28)1=(1+x+9)2
(3x+28)1=(1+x+9)2
Simplify.
3x+28=(1+x+9)2
3x+28=(1+x+9)2
Solve for x.
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Simplify (1+x+9)2.
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Rewrite (1+x+9)2 as (1+x+9)(1+x+9).
3x+28=(1+x+9)(1+x+9)
Expand (1+x+9)(1+x+9) using the FOIL Method.
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Apply the distributive property.
3x+28=1(1+x+9)+x+9(1+x+9)
Apply the distributive property.
3x+28=1⋅1+1x+9+x+9(1+x+9)
Apply the distributive property.
3x+28=1⋅1+1x+9+x+9⋅1+x+9x+9
3x+28=1⋅1+1x+9+x+9⋅1+x+9x+9
Simplify and combine like terms.
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Simplify each term.
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Multiply 1 by 1.
3x+28=1+1x+9+x+9⋅1+x+9x+9
Multiply x+9 by 1.
3x+28=1+x+9+x+9⋅1+x+9x+9
Multiply x+9 by 1.
3x+28=1+x+9+x+9+x+9x+9
Multiply x+9x+9.
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Raise x+9 to the power of 1.
3x+28=1+x+9+x+9+x+91x+9
Raise x+9 to the power of 1.
3x+28=1+x+9+x+9+x+91x+91
Use the power rule aman=am+n to combine exponents.
3x+28=1+x+9+x+9+x+91+1
Add 1 and 1.
3x+28=1+x+9+x+9+x+92
3x+28=1+x+9+x+9+x+92
Rewrite x+92 as x+9.
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Use axn=axn to rewrite x+9 as (x+9)12.
3x+28=1+x+9+x+9+((x+9)12)2
Apply the power rule and multiply exponents, (am)n=amn.
3x+28=1+x+9+x+9+(x+9)12⋅2
Combine 12 and 2.
3x+28=1+x+9+x+9+(x+9)22
Cancel the common factor of 2.
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Cancel the common factor.
3x+28=1+x+9+x+9+(x+9)22
Divide 1 by 1.
3x+28=1+x+9+x+9+(x+9)1
3x+28=1+x+9+x+9+(x+9)1
Simplify.
3x+28=1+x+9+x+9+x+9
3x+28=1+x+9+x+9+x+9
3x+28=1+x+9+x+9+x+9
Add 1 and 9.
3x+28=10+x+9+x+9+x
Add x+9 and x+9.
3x+28=10+2x+9+x
3x+28=10+2x+9+x
3x+28=10+2x+9+x
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
10+2x+9+x=3x+28
Move all terms not containing x+9 to the right side of the equation.
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Subtract 10 from both sides of the equation.
2x+9+x=3x+28-10
Subtract x from both sides of the equation.
2x+9=3x+28-10-x
Subtract x from 3x.
2x+9=2x+28-10
Subtract 10 from 28.
2x+9=2x+18
2x+9=2x+18
Divide each term by 2 and simplify.
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Divide each term in 2x+9=2x+18 by 2.
2x+92=2×2+182
Cancel the common factor of 2.
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Cancel the common factor.
2x+92=2×2+182
Divide x+9 by 1.
x+9=2×2+182
x+9=2×2+182
Simplify each term.
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Cancel the common factor of 2.
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Cancel the common factor.
x+9=2×2+182
Divide x by 1.
x+9=x+182
x+9=x+182
Divide 18 by 2.
x+9=x+9
x+9=x+9
x+9=x+9
To remove the radical on the left side of the equation, square both sides of the equation.
x+92=(x+9)2
Simplify each side of the equation.
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Multiply the exponents in ((x+9)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(x+9)12⋅2=(x+9)2
Cancel the common factor of 2.
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Cancel the common factor.
(x+9)12⋅2=(x+9)2
Rewrite the expression.
(x+9)1=(x+9)2
(x+9)1=(x+9)2
(x+9)1=(x+9)2
Simplify.
x+9=(x+9)2
x+9=(x+9)2
Solve for x.
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Simplify (x+9)2.
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Rewrite (x+9)2 as (x+9)(x+9).
x+9=(x+9)(x+9)
Expand (x+9)(x+9) using the FOIL Method.
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Apply the distributive property.
x+9=x(x+9)+9(x+9)
Apply the distributive property.
x+9=x⋅x+x⋅9+9(x+9)
Apply the distributive property.
x+9=x⋅x+x⋅9+9x+9⋅9
x+9=x⋅x+x⋅9+9x+9⋅9
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
x+9=x2+x⋅9+9x+9⋅9
Move 9 to the left of x.
x+9=x2+9⋅x+9x+9⋅9
Multiply 9 by 9.
x+9=x2+9x+9x+81
x+9=x2+9x+9x+81
Add 9x and 9x.
x+9=x2+18x+81
x+9=x2+18x+81
x+9=x2+18x+81
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
x2+18x+81=x+9
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+18x+81-x=9
Subtract x from 18x.
x2+17x+81=9
x2+17x+81=9
Move 9 to the left side of the equation by subtracting it from both sides.
x2+17x+81-9=0
Subtract 9 from 81.
x2+17x+72=0
Factor x2+17x+72 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 72 and whose sum is 17.
8,9
Write the factored form using these integers.
(x+8)(x+9)=0
(x+8)(x+9)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x+8=0
x+9=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
x+8=0
Subtract 8 from both sides of the equation.
x=-8
x=-8
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
x+9=0
Subtract 9 from both sides of the equation.
x=-9
x=-9
The final solution is all the values that make (x+8)(x+9)=0 true.
x=-8,-9
x=-8,-9
x=-8,-9
Solve for x square root of 3x+28=1+ square root of x+9

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