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Simplifying 10x2 + -120x + -40 = 0 Reorder the terms: -40 + -120x + 10x2 = 0 Solving -40 + -120x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-4 + -12x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-4 + -12x + x2)' equal to zero and attempt to solve: Simplifying -4 + -12x + x2 = 0 Solving -4 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -12x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -12x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -12x + x2 = 0 + 4 -12x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -12x + x2 = 4 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 4 + 36 Reorder the terms: 36 + -12x + x2 = 4 + 36 Combine like terms: 4 + 36 = 40 36 + -12x + x2 = 40 Factor a perfect square on the left side: (x + -6)(x + -6) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -6) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -6 = 6.32455532 Simplifying x + -6 = 6.32455532 Reorder the terms: -6 + x = 6.32455532 Solving -6 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.32455532 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.32455532 + 6 x = 6.32455532 + 6 Combine like terms: 6.32455532 + 6 = 12.32455532 x = 12.32455532 Simplifying x = 12.32455532Subproblem 2
x + -6 = -6.32455532 Simplifying x + -6 = -6.32455532 Reorder the terms: -6 + x = -6.32455532 Solving -6 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.32455532 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.32455532 + 6 x = -6.32455532 + 6 Combine like terms: -6.32455532 + 6 = -0.32455532 x = -0.32455532 Simplifying x = -0.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.32455532, -0.32455532}Solution
x = {12.32455532, -0.32455532}
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