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Simplifying -2x2 + 8x + 142 = 0 Reorder the terms: 142 + 8x + -2x2 = 0 Solving 142 + 8x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(71 + 4x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(71 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 71 + 4x + -1x2 = 0 Solving 71 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -71 + -4x + x2 = 0 Move the constant term to the right: Add '71' to each side of the equation. -71 + -4x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -4x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -4x + x2 = 0 + 71 -4x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -4x + x2 = 71 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 71 + 4 Reorder the terms: 4 + -4x + x2 = 71 + 4 Combine like terms: 71 + 4 = 75 4 + -4x + x2 = 75 Factor a perfect square on the left side: (x + -2)(x + -2) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -2) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -2 = 8.660254038 Simplifying x + -2 = 8.660254038 Reorder the terms: -2 + x = 8.660254038 Solving -2 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.660254038 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.660254038 + 2 x = 8.660254038 + 2 Combine like terms: 8.660254038 + 2 = 10.660254038 x = 10.660254038 Simplifying x = 10.660254038Subproblem 2
x + -2 = -8.660254038 Simplifying x + -2 = -8.660254038 Reorder the terms: -2 + x = -8.660254038 Solving -2 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.660254038 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.660254038 + 2 x = -8.660254038 + 2 Combine like terms: -8.660254038 + 2 = -6.660254038 x = -6.660254038 Simplifying x = -6.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.660254038, -6.660254038}Solution
x = {10.660254038, -6.660254038}
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