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Simplifying 80 = -16x2 + 90x Reorder the terms: 80 = 90x + -16x2 Solving 80 = 90x + -16x2 Solving for variable 'x'. Reorder the terms: 80 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2 Combine like terms: 90x + -90x = 0 80 + -90x + 16x2 = 0 + -16x2 + 16x2 80 + -90x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 80 + -90x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -45x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -45x + 8x2)' equal to zero and attempt to solve: Simplifying 40 + -45x + 8x2 = 0 Solving 40 + -45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5 + -5.625x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.625x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5.625x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.625x + x2 = 0 + -5 -5.625x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.625x + x2 = -5 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = -5 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = -5 + 7.91015625 Combine like terms: -5 + 7.91015625 = 2.91015625 7.91015625 + -5.625x + x2 = 2.91015625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 2.91015625 Calculate the square root of the right side: 1.705918008 Break this problem into two subproblems by setting (x + -2.8125) equal to 1.705918008 and -1.705918008.Subproblem 1
x + -2.8125 = 1.705918008 Simplifying x + -2.8125 = 1.705918008 Reorder the terms: -2.8125 + x = 1.705918008 Solving -2.8125 + x = 1.705918008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 1.705918008 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 1.705918008 + 2.8125 x = 1.705918008 + 2.8125 Combine like terms: 1.705918008 + 2.8125 = 4.518418008 x = 4.518418008 Simplifying x = 4.518418008Subproblem 2
x + -2.8125 = -1.705918008 Simplifying x + -2.8125 = -1.705918008 Reorder the terms: -2.8125 + x = -1.705918008 Solving -2.8125 + x = -1.705918008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -1.705918008 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -1.705918008 + 2.8125 x = -1.705918008 + 2.8125 Combine like terms: -1.705918008 + 2.8125 = 1.106581992 x = 1.106581992 Simplifying x = 1.106581992Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.518418008, 1.106581992}Solution
x = {4.518418008, 1.106581992}
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