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Simplifying 2x2 + -18x + -136 = 0 Reorder the terms: -136 + -18x + 2x2 = 0 Solving -136 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-68 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-68 + -9x + x2)' equal to zero and attempt to solve: Simplifying -68 + -9x + x2 = 0 Solving -68 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + -9x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + -9x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -9x + x2 = 0 + 68 -9x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 -9x + x2 = 68 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 68 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 68 + 20.25 Combine like terms: 68 + 20.25 = 88.25 20.25 + -9x + x2 = 88.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x + -4.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x + -4.5 = 9.394147114 Simplifying x + -4.5 = 9.394147114 Reorder the terms: -4.5 + x = 9.394147114 Solving -4.5 + x = 9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 9.394147114 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 9.394147114 + 4.5 x = 9.394147114 + 4.5 Combine like terms: 9.394147114 + 4.5 = 13.894147114 x = 13.894147114 Simplifying x = 13.894147114Subproblem 2
x + -4.5 = -9.394147114 Simplifying x + -4.5 = -9.394147114 Reorder the terms: -4.5 + x = -9.394147114 Solving -4.5 + x = -9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -9.394147114 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -9.394147114 + 4.5 x = -9.394147114 + 4.5 Combine like terms: -9.394147114 + 4.5 = -4.894147114 x = -4.894147114 Simplifying x = -4.894147114Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.894147114, -4.894147114}Solution
x = {13.894147114, -4.894147114}
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