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Simplifying 2x2 + 8x + -240 = 0 Reorder the terms: -240 + 8x + 2x2 = 0 Solving -240 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-120 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + 4x + x2)' equal to zero and attempt to solve: Simplifying -120 + 4x + x2 = 0 Solving -120 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 4x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 4x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 4x + x2 = 0 + 120 4x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 4x + x2 = 120 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 = 120 + 4 Reorder the terms: 4 + 4x + x2 = 120 + 4 Combine like terms: 120 + 4 = 124 4 + 4x + x2 = 124 Factor a perfect square on the left side: (x + 2)(x + 2) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + 2) equal to 11.135528726 and -11.135528726.Subproblem 1
x + 2 = 11.135528726 Simplifying x + 2 = 11.135528726 Reorder the terms: 2 + x = 11.135528726 Solving 2 + x = 11.135528726 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 = 11.135528726 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.135528726 + -2 x = 11.135528726 + -2 Combine like terms: 11.135528726 + -2 = 9.135528726 x = 9.135528726 Simplifying x = 9.135528726Subproblem 2
x + 2 = -11.135528726 Simplifying x + 2 = -11.135528726 Reorder the terms: 2 + x = -11.135528726 Solving 2 + x = -11.135528726 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 = -11.135528726 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.135528726 + -2 x = -11.135528726 + -2 Combine like terms: -11.135528726 + -2 = -13.135528726 x = -13.135528726 Simplifying x = -13.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.135528726, -13.135528726}Solution
x = {9.135528726, -13.135528726}
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