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Simplifying 0 = -16x2 + 120x + 6 Reorder the terms: 0 = 6 + 120x + -16x2 Solving 0 = 6 + 120x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -120x + 16x2 = 6 + 120x + -16x2 + -6 + -120x + 16x2 Reorder the terms: -6 + -120x + 16x2 = 6 + -6 + 120x + -120x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -120x + 16x2 = 0 + 120x + -120x + -16x2 + 16x2 -6 + -120x + 16x2 = 120x + -120x + -16x2 + 16x2 Combine like terms: 120x + -120x = 0 -6 + -120x + 16x2 = 0 + -16x2 + 16x2 -6 + -120x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -120x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -60x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -60x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -60x + 8x2 = 0 Solving -3 + -60x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -7.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -7.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -7.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -7.5x + x2 = 0 + 0.375 -7.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -7.5x + x2 = 0.375 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 0.375 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 0.375 + 14.0625 Combine like terms: 0.375 + 14.0625 = 14.4375 14.0625 + -7.5x + x2 = 14.4375 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 14.4375 Calculate the square root of the right side: 3.799671038 Break this problem into two subproblems by setting (x + -3.75) equal to 3.799671038 and -3.799671038.Subproblem 1
x + -3.75 = 3.799671038 Simplifying x + -3.75 = 3.799671038 Reorder the terms: -3.75 + x = 3.799671038 Solving -3.75 + x = 3.799671038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.799671038 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.799671038 + 3.75 x = 3.799671038 + 3.75 Combine like terms: 3.799671038 + 3.75 = 7.549671038 x = 7.549671038 Simplifying x = 7.549671038Subproblem 2
x + -3.75 = -3.799671038 Simplifying x + -3.75 = -3.799671038 Reorder the terms: -3.75 + x = -3.799671038 Solving -3.75 + x = -3.799671038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.799671038 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.799671038 + 3.75 x = -3.799671038 + 3.75 Combine like terms: -3.799671038 + 3.75 = -0.049671038 x = -0.049671038 Simplifying x = -0.049671038Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.549671038, -0.049671038}Solution
x = {7.549671038, -0.049671038}
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