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Simplifying 0 = -16x2 + 10x + 36 Reorder the terms: 0 = 36 + 10x + -16x2 Solving 0 = 36 + 10x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -36 = -36 -36 + -10x + 16x2 = 36 + 10x + -16x2 + -36 + -10x + 16x2 Reorder the terms: -36 + -10x + 16x2 = 36 + -36 + 10x + -10x + -16x2 + 16x2 Combine like terms: 36 + -36 = 0 -36 + -10x + 16x2 = 0 + 10x + -10x + -16x2 + 16x2 -36 + -10x + 16x2 = 10x + -10x + -16x2 + 16x2 Combine like terms: 10x + -10x = 0 -36 + -10x + 16x2 = 0 + -16x2 + 16x2 -36 + -10x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -36 + -10x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -5x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying -18 + -5x + 8x2 = 0 Solving -18 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + -0.625x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.625x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.625x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.625x + x2 = 0 + 2.25 -0.625x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.625x + x2 = 2.25 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 2.25 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 2.25 + 0.09765625 Combine like terms: 2.25 + 0.09765625 = 2.34765625 0.09765625 + -0.625x + x2 = 2.34765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 2.34765625 Calculate the square root of the right side: 1.532206334 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.532206334 and -1.532206334.Subproblem 1
x + -0.3125 = 1.532206334 Simplifying x + -0.3125 = 1.532206334 Reorder the terms: -0.3125 + x = 1.532206334 Solving -0.3125 + x = 1.532206334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.532206334 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.532206334 + 0.3125 x = 1.532206334 + 0.3125 Combine like terms: 1.532206334 + 0.3125 = 1.844706334 x = 1.844706334 Simplifying x = 1.844706334Subproblem 2
x + -0.3125 = -1.532206334 Simplifying x + -0.3125 = -1.532206334 Reorder the terms: -0.3125 + x = -1.532206334 Solving -0.3125 + x = -1.532206334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.532206334 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.532206334 + 0.3125 x = -1.532206334 + 0.3125 Combine like terms: -1.532206334 + 0.3125 = -1.219706334 x = -1.219706334 Simplifying x = -1.219706334Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.844706334, -1.219706334}Solution
x = {1.844706334, -1.219706334}
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