10x^2-132x-10=0

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


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

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

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

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -66x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + -66x + 5x2 = 0 Solving -5 + -66x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -13.2x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -13.2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -13.2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -13.2x + x2 = 0 + 1 -13.2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -13.2x + x2 = 1 The x term is -13.2x. Take half its coefficient (-6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. -13.2x + 43.56 + x2 = 1 + 43.56 Reorder the terms: 43.56 + -13.2x + x2 = 1 + 43.56 Combine like terms: 1 + 43.56 = 44.56 43.56 + -13.2x + x2 = 44.56 Factor a perfect square on the left side: (x + -6.6)(x + -6.6) = 44.56 Calculate the square root of the right side: 6.675327707 Break this problem into two subproblems by setting (x + -6.6) equal to 6.675327707 and -6.675327707.

Subproblem 1

x + -6.6 = 6.675327707 Simplifying x + -6.6 = 6.675327707 Reorder the terms: -6.6 + x = 6.675327707 Solving -6.6 + x = 6.675327707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + x = 6.675327707 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + x = 6.675327707 + 6.6 x = 6.675327707 + 6.6 Combine like terms: 6.675327707 + 6.6 = 13.275327707 x = 13.275327707 Simplifying x = 13.275327707

Subproblem 2

x + -6.6 = -6.675327707 Simplifying x + -6.6 = -6.675327707 Reorder the terms: -6.6 + x = -6.675327707 Solving -6.6 + x = -6.675327707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + x = -6.675327707 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + x = -6.675327707 + 6.6 x = -6.675327707 + 6.6 Combine like terms: -6.675327707 + 6.6 = -0.075327707 x = -0.075327707 Simplifying x = -0.075327707

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.275327707, -0.075327707}

Solution

x = {13.275327707, -0.075327707}

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