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Simplifying 4x2 + -2x + -120 = 0 Reorder the terms: -120 + -2x + 4x2 = 0 Solving -120 + -2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -60 + -1x + 2x2 = 0 Solving -60 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30 + -0.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -0.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -0.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -0.5x + x2 = 0 + 30 -0.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -0.5x + x2 = 30 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 30 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 30 + 0.0625 Combine like terms: 30 + 0.0625 = 30.0625 0.0625 + -0.5x + x2 = 30.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (x + -0.25) equal to 5.48292805 and -5.48292805.Subproblem 1
x + -0.25 = 5.48292805 Simplifying x + -0.25 = 5.48292805 Reorder the terms: -0.25 + x = 5.48292805 Solving -0.25 + x = 5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.48292805 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.48292805 + 0.25 x = 5.48292805 + 0.25 Combine like terms: 5.48292805 + 0.25 = 5.73292805 x = 5.73292805 Simplifying x = 5.73292805Subproblem 2
x + -0.25 = -5.48292805 Simplifying x + -0.25 = -5.48292805 Reorder the terms: -0.25 + x = -5.48292805 Solving -0.25 + x = -5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.48292805 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.48292805 + 0.25 x = -5.48292805 + 0.25 Combine like terms: -5.48292805 + 0.25 = -5.23292805 x = -5.23292805 Simplifying x = -5.23292805Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.73292805, -5.23292805}Solution
x = {5.73292805, -5.23292805}
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