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Simplifying 3x2 + -39x + -87 = 0 Reorder the terms: -87 + -39x + 3x2 = 0 Solving -87 + -39x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-29 + -13x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-29 + -13x + x2)' equal to zero and attempt to solve: Simplifying -29 + -13x + x2 = 0 Solving -29 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -13x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -13x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -13x + x2 = 0 + 29 -13x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -13x + x2 = 29 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 29 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 29 + 42.25 Combine like terms: 29 + 42.25 = 71.25 42.25 + -13x + x2 = 71.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + -6.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + -6.5 = 8.440971508 Simplifying x + -6.5 = 8.440971508 Reorder the terms: -6.5 + x = 8.440971508 Solving -6.5 + x = 8.440971508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.440971508 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.440971508 + 6.5 x = 8.440971508 + 6.5 Combine like terms: 8.440971508 + 6.5 = 14.940971508 x = 14.940971508 Simplifying x = 14.940971508Subproblem 2
x + -6.5 = -8.440971508 Simplifying x + -6.5 = -8.440971508 Reorder the terms: -6.5 + x = -8.440971508 Solving -6.5 + x = -8.440971508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.440971508 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.440971508 + 6.5 x = -8.440971508 + 6.5 Combine like terms: -8.440971508 + 6.5 = -1.940971508 x = -1.940971508 Simplifying x = -1.940971508Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.940971508, -1.940971508}Solution
x = {14.940971508, -1.940971508}
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