(x-7)(x-7)=29-x^2

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Solution for (x-7)(x-7)=29-x^2 equation: 


Simplifying
(x + -7)(x + -7) = 29 + -1x2

Reorder the terms:
(-7 + x)(x + -7) = 29 + -1x2

Reorder the terms:
(-7 + x)(-7 + x) = 29 + -1x2

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 29 + -1x2
((-7 * -7 + x * -7) + x(-7 + x)) = 29 + -1x2
((49 + -7x) + x(-7 + x)) = 29 + -1x2
(49 + -7x + (-7 * x + x * x)) = 29 + -1x2
(49 + -7x + (-7x + x2)) = 29 + -1x2

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 29 + -1x2

Solving
49 + -14x + x2 = 29 + -1x2

Solving for variable 'x'.

Reorder the terms:
49 + -29 + -14x + x2 + x2 = 29 + -1x2 + -29 + x2

Combine like terms: 49 + -29 = 20
20 + -14x + x2 + x2 = 29 + -1x2 + -29 + x2

Combine like terms: x2 + x2 = 2x2
20 + -14x + 2x2 = 29 + -1x2 + -29 + x2

Reorder the terms:
20 + -14x + 2x2 = 29 + -29 + -1x2 + x2

Combine like terms: 29 + -29 = 0
20 + -14x + 2x2 = 0 + -1x2 + x2
20 + -14x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
20 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7x + x2) = 0

Factor a trinomial.
2((2 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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