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Simplifying -16x2 + 62x + 9 = 17 Reorder the terms: 9 + 62x + -16x2 = 17 Solving 9 + 62x + -16x2 = 17 Solving for variable 'x'. Reorder the terms: 9 + -17 + 62x + -16x2 = 17 + -17 Combine like terms: 9 + -17 = -8 -8 + 62x + -16x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -8 + 62x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 31x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 31x + -8x2)' equal to zero and attempt to solve: Simplifying -4 + 31x + -8x2 = 0 Solving -4 + 31x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.5 + -3.875x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.875x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.875x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.875x + x2 = 0 + -0.5 -3.875x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.875x + x2 = -0.5 The x term is -3.875x. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875x + 3.75390625 + x2 = -0.5 + 3.75390625 Reorder the terms: 3.75390625 + -3.875x + x2 = -0.5 + 3.75390625 Combine like terms: -0.5 + 3.75390625 = 3.25390625 3.75390625 + -3.875x + x2 = 3.25390625 Factor a perfect square on the left side: (x + -1.9375)(x + -1.9375) = 3.25390625 Calculate the square root of the right side: 1.803858711 Break this problem into two subproblems by setting (x + -1.9375) equal to 1.803858711 and -1.803858711.Subproblem 1
x + -1.9375 = 1.803858711 Simplifying x + -1.9375 = 1.803858711 Reorder the terms: -1.9375 + x = 1.803858711 Solving -1.9375 + x = 1.803858711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = 1.803858711 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = 1.803858711 + 1.9375 x = 1.803858711 + 1.9375 Combine like terms: 1.803858711 + 1.9375 = 3.741358711 x = 3.741358711 Simplifying x = 3.741358711Subproblem 2
x + -1.9375 = -1.803858711 Simplifying x + -1.9375 = -1.803858711 Reorder the terms: -1.9375 + x = -1.803858711 Solving -1.9375 + x = -1.803858711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = -1.803858711 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = -1.803858711 + 1.9375 x = -1.803858711 + 1.9375 Combine like terms: -1.803858711 + 1.9375 = 0.133641289 x = 0.133641289 Simplifying x = 0.133641289Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.741358711, 0.133641289}Solution
x = {3.741358711, 0.133641289}
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