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Simplifying 0 = -16x2 + 80x + 18 Reorder the terms: 0 = 18 + 80x + -16x2 Solving 0 = 18 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -18 = -18 -18 + -80x + 16x2 = 18 + 80x + -16x2 + -18 + -80x + 16x2 Reorder the terms: -18 + -80x + 16x2 = 18 + -18 + 80x + -80x + -16x2 + 16x2 Combine like terms: 18 + -18 = 0 -18 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 -18 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 -18 + -80x + 16x2 = 0 + -16x2 + 16x2 -18 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -18 + -80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -40x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -40x + 8x2)' equal to zero and attempt to solve: Simplifying -9 + -40x + 8x2 = 0 Solving -9 + -40x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -5x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -5x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -5x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -5x + x2 = 0 + 1.125 -5x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -5x + x2 = 1.125 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 = 1.125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.125 + 6.25 Combine like terms: 1.125 + 6.25 = 7.375 6.25 + -5x + x2 = 7.375 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.375 Calculate the square root of the right side: 2.715695123 Break this problem into two subproblems by setting (x + -2.5) equal to 2.715695123 and -2.715695123.Subproblem 1
x + -2.5 = 2.715695123 Simplifying x + -2.5 = 2.715695123 Reorder the terms: -2.5 + x = 2.715695123 Solving -2.5 + x = 2.715695123 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 = 2.715695123 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.715695123 + 2.5 x = 2.715695123 + 2.5 Combine like terms: 2.715695123 + 2.5 = 5.215695123 x = 5.215695123 Simplifying x = 5.215695123Subproblem 2
x + -2.5 = -2.715695123 Simplifying x + -2.5 = -2.715695123 Reorder the terms: -2.5 + x = -2.715695123 Solving -2.5 + x = -2.715695123 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 = -2.715695123 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.715695123 + 2.5 x = -2.715695123 + 2.5 Combine like terms: -2.715695123 + 2.5 = -0.215695123 x = -0.215695123 Simplifying x = -0.215695123Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.215695123, -0.215695123}Solution
x = {5.215695123, -0.215695123}
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