10x^2-10x-132=0

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Solution for 10x^2-10x-132=0 equation:


Simplifying
10x2 + -10x + -132 = 0

Reorder the terms:
-132 + -10x + 10x2 = 0

Solving
-132 + -10x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + -5x + 5x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-66 + -5x + 5x2)' equal to zero and attempt to solve: Simplifying -66 + -5x + 5x2 = 0 Solving -66 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -13.2 + -1x + x2 = 0 Move the constant term to the right: Add '13.2' to each side of the equation. -13.2 + -1x + 13.2 + x2 = 0 + 13.2 Reorder the terms: -13.2 + 13.2 + -1x + x2 = 0 + 13.2 Combine like terms: -13.2 + 13.2 = 0.0 0.0 + -1x + x2 = 0 + 13.2 -1x + x2 = 0 + 13.2 Combine like terms: 0 + 13.2 = 13.2 -1x + x2 = 13.2 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 13.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 13.2 + 0.25 Combine like terms: 13.2 + 0.25 = 13.45 0.25 + -1x + x2 = 13.45 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 13.45 Calculate the square root of the right side: 3.667424164 Break this problem into two subproblems by setting (x + -0.5) equal to 3.667424164 and -3.667424164.

Subproblem 1

x + -0.5 = 3.667424164 Simplifying x + -0.5 = 3.667424164 Reorder the terms: -0.5 + x = 3.667424164 Solving -0.5 + x = 3.667424164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.667424164 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.667424164 + 0.5 x = 3.667424164 + 0.5 Combine like terms: 3.667424164 + 0.5 = 4.167424164 x = 4.167424164 Simplifying x = 4.167424164

Subproblem 2

x + -0.5 = -3.667424164 Simplifying x + -0.5 = -3.667424164 Reorder the terms: -0.5 + x = -3.667424164 Solving -0.5 + x = -3.667424164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.667424164 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.667424164 + 0.5 x = -3.667424164 + 0.5 Combine like terms: -3.667424164 + 0.5 = -3.167424164 x = -3.167424164 Simplifying x = -3.167424164

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.167424164, -3.167424164}

Solution

x = {4.167424164, -3.167424164}

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