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Simplifying 0 = -16x2 + 2x + 360 Reorder the terms: 0 = 360 + 2x + -16x2 Solving 0 = 360 + 2x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -360 = -360 -360 + -2x + 16x2 = 360 + 2x + -16x2 + -360 + -2x + 16x2 Reorder the terms: -360 + -2x + 16x2 = 360 + -360 + 2x + -2x + -16x2 + 16x2 Combine like terms: 360 + -360 = 0 -360 + -2x + 16x2 = 0 + 2x + -2x + -16x2 + 16x2 -360 + -2x + 16x2 = 2x + -2x + -16x2 + 16x2 Combine like terms: 2x + -2x = 0 -360 + -2x + 16x2 = 0 + -16x2 + 16x2 -360 + -2x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -360 + -2x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-180 + -1x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-180 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying -180 + -1x + 8x2 = 0 Solving -180 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -22.5 + -0.125x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -0.125x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -0.125x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -0.125x + x2 = 0 + 22.5 -0.125x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -0.125x + x2 = 22.5 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 22.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 22.5 + 0.00390625 Combine like terms: 22.5 + 0.00390625 = 22.50390625 0.00390625 + -0.125x + x2 = 22.50390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 22.50390625 Calculate the square root of the right side: 4.743828227 Break this problem into two subproblems by setting (x + -0.0625) equal to 4.743828227 and -4.743828227.Subproblem 1
x + -0.0625 = 4.743828227 Simplifying x + -0.0625 = 4.743828227 Reorder the terms: -0.0625 + x = 4.743828227 Solving -0.0625 + x = 4.743828227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 4.743828227 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 4.743828227 + 0.0625 x = 4.743828227 + 0.0625 Combine like terms: 4.743828227 + 0.0625 = 4.806328227 x = 4.806328227 Simplifying x = 4.806328227Subproblem 2
x + -0.0625 = -4.743828227 Simplifying x + -0.0625 = -4.743828227 Reorder the terms: -0.0625 + x = -4.743828227 Solving -0.0625 + x = -4.743828227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -4.743828227 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -4.743828227 + 0.0625 x = -4.743828227 + 0.0625 Combine like terms: -4.743828227 + 0.0625 = -4.681328227 x = -4.681328227 Simplifying x = -4.681328227Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.806328227, -4.681328227}Solution
x = {4.806328227, -4.681328227}
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