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Simplifying 0 = -16x2 + 80x + 10 Reorder the terms: 0 = 10 + 80x + -16x2 Solving 0 = 10 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -80x + 16x2 = 10 + 80x + -16x2 + -10 + -80x + 16x2 Reorder the terms: -10 + -80x + 16x2 = 10 + -10 + 80x + -80x + -16x2 + 16x2 Combine like terms: 10 + -10 = 0 -10 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 -10 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 -10 + -80x + 16x2 = 0 + -16x2 + 16x2 -10 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -10 + -80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -40x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -40x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + -40x + 8x2 = 0 Solving -5 + -40x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -5x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -5x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -5x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -5x + x2 = 0 + 0.625 -5x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -5x + x2 = 0.625 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.625 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.625 + 6.25 Combine like terms: 0.625 + 6.25 = 6.875 6.25 + -5x + x2 = 6.875 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.875 Calculate the square root of the right side: 2.62202212 Break this problem into two subproblems by setting (x + -2.5) equal to 2.62202212 and -2.62202212.Subproblem 1
x + -2.5 = 2.62202212 Simplifying x + -2.5 = 2.62202212 Reorder the terms: -2.5 + x = 2.62202212 Solving -2.5 + x = 2.62202212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.62202212 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.62202212 + 2.5 x = 2.62202212 + 2.5 Combine like terms: 2.62202212 + 2.5 = 5.12202212 x = 5.12202212 Simplifying x = 5.12202212Subproblem 2
x + -2.5 = -2.62202212 Simplifying x + -2.5 = -2.62202212 Reorder the terms: -2.5 + x = -2.62202212 Solving -2.5 + x = -2.62202212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.62202212 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.62202212 + 2.5 x = -2.62202212 + 2.5 Combine like terms: -2.62202212 + 2.5 = -0.12202212 x = -0.12202212 Simplifying x = -0.12202212Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.12202212, -0.12202212}Solution
x = {5.12202212, -0.12202212}
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