-2(x-5)(x-5)-7=1

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Solution for -2(x-5)(x-5)-7=1 equation:


Simplifying
-2(x + -5)(x + -5) + -7 = 1

Reorder the terms:
-2(-5 + x)(x + -5) + -7 = 1

Reorder the terms:
-2(-5 + x)(-5 + x) + -7 = 1

Multiply (-5 + x) * (-5 + x)
-2(-5(-5 + x) + x(-5 + x)) + -7 = 1
-2((-5 * -5 + x * -5) + x(-5 + x)) + -7 = 1
-2((25 + -5x) + x(-5 + x)) + -7 = 1
-2(25 + -5x + (-5 * x + x * x)) + -7 = 1
-2(25 + -5x + (-5x + x2)) + -7 = 1

Combine like terms: -5x + -5x = -10x
-2(25 + -10x + x2) + -7 = 1
(25 * -2 + -10x * -2 + x2 * -2) + -7 = 1
(-50 + 20x + -2x2) + -7 = 1

Reorder the terms:
-50 + -7 + 20x + -2x2 = 1

Combine like terms: -50 + -7 = -57
-57 + 20x + -2x2 = 1

Solving
-57 + 20x + -2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-57 + -1 + 20x + -2x2 = 1 + -1

Combine like terms: -57 + -1 = -58
-58 + 20x + -2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-58 + 20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + 10x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-29 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -29 + 10x + -1x2 = 0 Solving -29 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 29 + -10x + x2 = 0 Move the constant term to the right: Add '-29' to each side of the equation. 29 + -10x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + -10x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -10x + x2 = 0 + -29 -10x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 -10x + x2 = -29 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -29 + 25 Reorder the terms: 25 + -10x + x2 = -29 + 25 Combine like terms: -29 + 25 = -4 25 + -10x + x2 = -4 Factor a perfect square on the left side: (x + -5)(x + -5) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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