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Simplifying 15x2 + -20x + -240 = 0 Reorder the terms: -240 + -20x + 15x2 = 0 Solving -240 + -20x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-48 + -4x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-48 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying -48 + -4x + 3x2 = 0 Solving -48 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -1.333333333x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -1.333333333x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1.333333333x + x2 = 0 + 16 -1.333333333x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1.333333333x + x2 = 16 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 16 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 16 + 0.4444444442 Combine like terms: 16 + 0.4444444442 = 16.4444444442 0.4444444442 + -1.333333333x + x2 = 16.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 16.4444444442 Calculate the square root of the right side: 4.05517502 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 4.05517502 and -4.05517502.Subproblem 1
x + -0.6666666665 = 4.05517502 Simplifying x + -0.6666666665 = 4.05517502 Reorder the terms: -0.6666666665 + x = 4.05517502 Solving -0.6666666665 + x = 4.05517502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 4.05517502 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 4.05517502 + 0.6666666665 x = 4.05517502 + 0.6666666665 Combine like terms: 4.05517502 + 0.6666666665 = 4.7218416865 x = 4.7218416865 Simplifying x = 4.7218416865Subproblem 2
x + -0.6666666665 = -4.05517502 Simplifying x + -0.6666666665 = -4.05517502 Reorder the terms: -0.6666666665 + x = -4.05517502 Solving -0.6666666665 + x = -4.05517502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -4.05517502 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -4.05517502 + 0.6666666665 x = -4.05517502 + 0.6666666665 Combine like terms: -4.05517502 + 0.6666666665 = -3.3885083535 x = -3.3885083535 Simplifying x = -3.3885083535Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.7218416865, -3.3885083535}Solution
x = {4.7218416865, -3.3885083535}
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