Solve using the Square Root Property 5 square root of 5x+29=x+3

Math
55x+29=x+3
To remove the radical on the left side of the equation, square both sides of the equation.
(55x+29)2=(x+3)2
Simplify each side of the equation.
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Apply the product rule to 5(5x+29)12.
52((5x+29)12)2=(x+3)2
Raise 5 to the power of 2.
25((5x+29)12)2=(x+3)2
Multiply the exponents in ((5x+29)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
25(5x+29)12⋅2=(x+3)2
Cancel the common factor of 2.
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Cancel the common factor.
25(5x+29)12⋅2=(x+3)2
Rewrite the expression.
25(5x+29)1=(x+3)2
25(5x+29)1=(x+3)2
25(5x+29)1=(x+3)2
Simplify.
25(5x+29)=(x+3)2
Apply the distributive property.
25(5x)+25⋅29=(x+3)2
Multiply 5 by 25.
125x+25⋅29=(x+3)2
Multiply 25 by 29.
125x+725=(x+3)2
125x+725=(x+3)2
Solve for x.
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Simplify (x+3)2.
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Rewrite (x+3)2 as (x+3)(x+3).
125x+725=(x+3)(x+3)
Expand (x+3)(x+3) using the FOIL Method.
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Apply the distributive property.
125x+725=x(x+3)+3(x+3)
Apply the distributive property.
125x+725=x⋅x+x⋅3+3(x+3)
Apply the distributive property.
125x+725=x⋅x+x⋅3+3x+3⋅3
125x+725=x⋅x+x⋅3+3x+3⋅3
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
125x+725=x2+x⋅3+3x+3⋅3
Move 3 to the left of x.
125x+725=x2+3⋅x+3x+3⋅3
Multiply 3 by 3.
125x+725=x2+3x+3x+9
125x+725=x2+3x+3x+9
Add 3x and 3x.
125x+725=x2+6x+9
125x+725=x2+6x+9
125x+725=x2+6x+9
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
x2+6x+9=125x+725
Move all terms containing x to the left side of the equation.
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Subtract 125x from both sides of the equation.
x2+6x+9-125x=725
Subtract 125x from 6x.
x2-119x+9=725
x2-119x+9=725
Move all terms to the left side of the equation and simplify.
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Move 725 to the left side of the equation by subtracting it from both sides.
x2-119x+9-725=0
Subtract 725 from 9.
x2-119x-716=0
x2-119x-716=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-119, and c=-716 into the quadratic formula and solve for x.
119±(-119)2-4⋅(1⋅-716)2⋅1
Simplify.
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Simplify the numerator.
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Raise -119 to the power of 2.
x=119±14161-4⋅(1⋅-716)2⋅1
Multiply -716 by 1.
x=119±14161-4⋅-7162⋅1
Multiply -4 by -716.
x=119±14161+28642⋅1
Add 14161 and 2864.
x=119±170252⋅1
Rewrite 17025 as 52⋅681.
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Factor 25 out of 17025.
x=119±25(681)2⋅1
Rewrite 25 as 52.
x=119±52⋅6812⋅1
x=119±52⋅6812⋅1
Pull terms out from under the radical.
x=119±56812⋅1
x=119±56812⋅1
Multiply 2 by 1.
x=119±56812
x=119±56812
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -119 to the power of 2.
x=119±14161-4⋅(1⋅-716)2⋅1
Multiply -716 by 1.
x=119±14161-4⋅-7162⋅1
Multiply -4 by -716.
x=119±14161+28642⋅1
Add 14161 and 2864.
x=119±170252⋅1
Rewrite 17025 as 52⋅681.
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Factor 25 out of 17025.
x=119±25(681)2⋅1
Rewrite 25 as 52.
x=119±52⋅6812⋅1
x=119±52⋅6812⋅1
Pull terms out from under the radical.
x=119±56812⋅1
x=119±56812⋅1
Multiply 2 by 1.
x=119±56812
Change the ± to +.
x=119+56812
x=119+56812
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -119 to the power of 2.
x=119±14161-4⋅(1⋅-716)2⋅1
Multiply -716 by 1.
x=119±14161-4⋅-7162⋅1
Multiply -4 by -716.
x=119±14161+28642⋅1
Add 14161 and 2864.
x=119±170252⋅1
Rewrite 17025 as 52⋅681.
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Factor 25 out of 17025.
x=119±25(681)2⋅1
Rewrite 25 as 52.
x=119±52⋅6812⋅1
x=119±52⋅6812⋅1
Pull terms out from under the radical.
x=119±56812⋅1
x=119±56812⋅1
Multiply 2 by 1.
x=119±56812
Change the ± to -.
x=119-56812
x=119-56812
The final answer is the combination of both solutions.
x=119+56812,119-56812
x=119+56812,119-56812
Exclude the solutions that do not make 55x+29=x+3 true.
x=119+56812
The result can be shown in multiple forms.
Exact Form:
x=119+56812
Decimal Form:
x=124.73994175…
Solve using the Square Root Property 5 square root of 5x+29=x+3

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