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Simplifying 2x2 + 10x + -120 = 0 Reorder the terms: -120 + 10x + 2x2 = 0 Solving -120 + 10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 5x + x2)' equal to zero and attempt to solve: Simplifying -60 + 5x + x2 = 0 Solving -60 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 5x + x2 = 0 + 60 5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 5x + x2 = 60 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 60 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 60 + 6.25 Combine like terms: 60 + 6.25 = 66.25 6.25 + 5x + x2 = 66.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + 2.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + 2.5 = 8.139410298 Simplifying x + 2.5 = 8.139410298 Reorder the terms: 2.5 + x = 8.139410298 Solving 2.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.139410298 + -2.5 x = 8.139410298 + -2.5 Combine like terms: 8.139410298 + -2.5 = 5.639410298 x = 5.639410298 Simplifying x = 5.639410298Subproblem 2
x + 2.5 = -8.139410298 Simplifying x + 2.5 = -8.139410298 Reorder the terms: 2.5 + x = -8.139410298 Solving 2.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.139410298 + -2.5 x = -8.139410298 + -2.5 Combine like terms: -8.139410298 + -2.5 = -10.639410298 x = -10.639410298 Simplifying x = -10.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.639410298, -10.639410298}Solution
x = {5.639410298, -10.639410298}
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