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Simplifying 3 = -16x2 + 90x + -7 Reorder the terms: 3 = -7 + 90x + -16x2 Solving 3 = -7 + 90x + -16x2 Solving for variable 'x'. Combine like terms: 3 + 7 = 10 10 + -90x + 16x2 = -7 + 90x + -16x2 + 7 + -90x + 16x2 Reorder the terms: 10 + -90x + 16x2 = -7 + 7 + 90x + -90x + -16x2 + 16x2 Combine like terms: -7 + 7 = 0 10 + -90x + 16x2 = 0 + 90x + -90x + -16x2 + 16x2 10 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2 Combine like terms: 90x + -90x = 0 10 + -90x + 16x2 = 0 + -16x2 + 16x2 10 + -90x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 10 + -90x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -45x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -45x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -45x + 8x2 = 0 Solving 5 + -45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -5.625x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -5.625x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -5.625x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -5.625x + x2 = 0 + -0.625 -5.625x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -5.625x + x2 = -0.625 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 = -0.625 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = -0.625 + 7.91015625 Combine like terms: -0.625 + 7.91015625 = 7.28515625 7.91015625 + -5.625x + x2 = 7.28515625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 7.28515625 Calculate the square root of the right side: 2.69910286 Break this problem into two subproblems by setting (x + -2.8125) equal to 2.69910286 and -2.69910286.Subproblem 1
x + -2.8125 = 2.69910286 Simplifying x + -2.8125 = 2.69910286 Reorder the terms: -2.8125 + x = 2.69910286 Solving -2.8125 + x = 2.69910286 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 = 2.69910286 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 2.69910286 + 2.8125 x = 2.69910286 + 2.8125 Combine like terms: 2.69910286 + 2.8125 = 5.51160286 x = 5.51160286 Simplifying x = 5.51160286Subproblem 2
x + -2.8125 = -2.69910286 Simplifying x + -2.8125 = -2.69910286 Reorder the terms: -2.8125 + x = -2.69910286 Solving -2.8125 + x = -2.69910286 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 = -2.69910286 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -2.69910286 + 2.8125 x = -2.69910286 + 2.8125 Combine like terms: -2.69910286 + 2.8125 = 0.11339714 x = 0.11339714 Simplifying x = 0.11339714Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.51160286, 0.11339714}Solution
x = {5.51160286, 0.11339714}
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