2(x-5)(x-5)-7x-37=0

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Solution for 2(x-5)(x-5)-7x-37=0 equation: 


Simplifying
2(x + -5)(x + -5) + -7x + -37 = 0

Reorder the terms:
2(-5 + x)(x + -5) + -7x + -37 = 0

Reorder the terms:
2(-5 + x)(-5 + x) + -7x + -37 = 0

Multiply (-5 + x) * (-5 + x)
2(-5(-5 + x) + x(-5 + x)) + -7x + -37 = 0
2((-5 * -5 + x * -5) + x(-5 + x)) + -7x + -37 = 0
2((25 + -5x) + x(-5 + x)) + -7x + -37 = 0
2(25 + -5x + (-5 * x + x * x)) + -7x + -37 = 0
2(25 + -5x + (-5x + x2)) + -7x + -37 = 0

Combine like terms: -5x + -5x = -10x
2(25 + -10x + x2) + -7x + -37 = 0
(25 * 2 + -10x * 2 + x2 * 2) + -7x + -37 = 0
(50 + -20x + 2x2) + -7x + -37 = 0

Reorder the terms:
50 + -37 + -20x + -7x + 2x2 = 0

Combine like terms: 50 + -37 = 13
13 + -20x + -7x + 2x2 = 0

Combine like terms: -20x + -7x = -27x
13 + -27x + 2x2 = 0

Solving
13 + -27x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(13 + -1x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {0.5, 13}

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