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Simplifying -16x2 + 240x + 20 = 0 Reorder the terms: 20 + 240x + -16x2 = 0 Solving 20 + 240x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 60x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 60x + -4x2)' equal to zero and attempt to solve: Simplifying 5 + 60x + -4x2 = 0 Solving 5 + 60x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -15x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -15x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -15x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -15x + x2 = 0 + 1.25 -15x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -15x + x2 = 1.25 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 1.25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 1.25 + 56.25 Combine like terms: 1.25 + 56.25 = 57.5 56.25 + -15x + x2 = 57.5 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 57.5 Calculate the square root of the right side: 7.582875444 Break this problem into two subproblems by setting (x + -7.5) equal to 7.582875444 and -7.582875444.Subproblem 1
x + -7.5 = 7.582875444 Simplifying x + -7.5 = 7.582875444 Reorder the terms: -7.5 + x = 7.582875444 Solving -7.5 + x = 7.582875444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.582875444 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.582875444 + 7.5 x = 7.582875444 + 7.5 Combine like terms: 7.582875444 + 7.5 = 15.082875444 x = 15.082875444 Simplifying x = 15.082875444Subproblem 2
x + -7.5 = -7.582875444 Simplifying x + -7.5 = -7.582875444 Reorder the terms: -7.5 + x = -7.582875444 Solving -7.5 + x = -7.582875444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.582875444 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.582875444 + 7.5 x = -7.582875444 + 7.5 Combine like terms: -7.582875444 + 7.5 = -0.082875444 x = -0.082875444 Simplifying x = -0.082875444Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.082875444, -0.082875444}Solution
x = {15.082875444, -0.082875444}
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