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Simplifying -16x2 + 90x = 120 Reorder the terms: 90x + -16x2 = 120 Solving 90x + -16x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 90x + -16x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 90x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 45x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 45x + -8x2)' equal to zero and attempt to solve: Simplifying -60 + 45x + -8x2 = 0 Solving -60 + 45x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 7.5 + -5.625x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -5.625x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -5.625x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -5.625x + x2 = 0 + -7.5 -5.625x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -5.625x + x2 = -7.5 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 = -7.5 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = -7.5 + 7.91015625 Combine like terms: -7.5 + 7.91015625 = 0.41015625 7.91015625 + -5.625x + x2 = 0.41015625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 0.41015625 Calculate the square root of the right side: 0.640434423 Break this problem into two subproblems by setting (x + -2.8125) equal to 0.640434423 and -0.640434423.Subproblem 1
x + -2.8125 = 0.640434423 Simplifying x + -2.8125 = 0.640434423 Reorder the terms: -2.8125 + x = 0.640434423 Solving -2.8125 + x = 0.640434423 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 = 0.640434423 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 0.640434423 + 2.8125 x = 0.640434423 + 2.8125 Combine like terms: 0.640434423 + 2.8125 = 3.452934423 x = 3.452934423 Simplifying x = 3.452934423Subproblem 2
x + -2.8125 = -0.640434423 Simplifying x + -2.8125 = -0.640434423 Reorder the terms: -2.8125 + x = -0.640434423 Solving -2.8125 + x = -0.640434423 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 = -0.640434423 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -0.640434423 + 2.8125 x = -0.640434423 + 2.8125 Combine like terms: -0.640434423 + 2.8125 = 2.172065577 x = 2.172065577 Simplifying x = 2.172065577Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.452934423, 2.172065577}Solution
x = {3.452934423, 2.172065577}
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