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Simplifying 0 = -16x2 + 40x + 2 Reorder the terms: 0 = 2 + 40x + -16x2 Solving 0 = 2 + 40x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -40x + 16x2 = 2 + 40x + -16x2 + -2 + -40x + 16x2 Reorder the terms: -2 + -40x + 16x2 = 2 + -2 + 40x + -40x + -16x2 + 16x2 Combine like terms: 2 + -2 = 0 -2 + -40x + 16x2 = 0 + 40x + -40x + -16x2 + 16x2 -2 + -40x + 16x2 = 40x + -40x + -16x2 + 16x2 Combine like terms: 40x + -40x = 0 -2 + -40x + 16x2 = 0 + -16x2 + 16x2 -2 + -40x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2 + -40x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -20x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -20x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + -20x + 8x2 = 0 Solving -1 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -2.5x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -2.5x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -2.5x + x2 = 0 + 0.125 -2.5x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -2.5x + x2 = 0.125 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.125 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.125 + 1.5625 Combine like terms: 0.125 + 1.5625 = 1.6875 1.5625 + -2.5x + x2 = 1.6875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (x + -1.25) equal to 1.299038106 and -1.299038106.Subproblem 1
x + -1.25 = 1.299038106 Simplifying x + -1.25 = 1.299038106 Reorder the terms: -1.25 + x = 1.299038106 Solving -1.25 + x = 1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.299038106 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.299038106 + 1.25 x = 1.299038106 + 1.25 Combine like terms: 1.299038106 + 1.25 = 2.549038106 x = 2.549038106 Simplifying x = 2.549038106Subproblem 2
x + -1.25 = -1.299038106 Simplifying x + -1.25 = -1.299038106 Reorder the terms: -1.25 + x = -1.299038106 Solving -1.25 + x = -1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.299038106 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.299038106 + 1.25 x = -1.299038106 + 1.25 Combine like terms: -1.299038106 + 1.25 = -0.049038106 x = -0.049038106 Simplifying x = -0.049038106Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.549038106, -0.049038106}Solution
x = {2.549038106, -0.049038106}
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