x^2-14x+49+x^2=169

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Solution for x^2-14x+49+x^2=169 equation:


Simplifying
x2 + -14x + 49 + x2 = 169

Reorder the terms:
49 + -14x + x2 + x2 = 169

Combine like terms: x2 + x2 = 2x2
49 + -14x + 2x2 = 169

Solving
49 + -14x + 2x2 = 169

Solving for variable 'x'.

Reorder the terms:
49 + -169 + -14x + 2x2 = 169 + -169

Combine like terms: 49 + -169 = -120
-120 + -14x + 2x2 = 169 + -169

Combine like terms: 169 + -169 = 0
-120 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -7x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(12 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12

Solution

x = {-5, 12}

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