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Simplifying 0 = 116 + 64x + -16x2 Solving 0 = 116 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -116 = -116 -116 + -64x + 16x2 = 116 + 64x + -16x2 + -116 + -64x + 16x2 Reorder the terms: -116 + -64x + 16x2 = 116 + -116 + 64x + -64x + -16x2 + 16x2 Combine like terms: 116 + -116 = 0 -116 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -116 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -116 + -64x + 16x2 = 0 + -16x2 + 16x2 -116 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -116 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-29 + -16x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-29 + -16x + 4x2)' equal to zero and attempt to solve: Simplifying -29 + -16x + 4x2 = 0 Solving -29 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -4x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -4x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -4x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -4x + x2 = 0 + 7.25 -4x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -4x + x2 = 7.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 7.25 + 4 Reorder the terms: 4 + -4x + x2 = 7.25 + 4 Combine like terms: 7.25 + 4 = 11.25 4 + -4x + x2 = 11.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -2) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -2 = 3.354101966 Simplifying x + -2 = 3.354101966 Reorder the terms: -2 + x = 3.354101966 Solving -2 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.354101966 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.354101966 + 2 x = 3.354101966 + 2 Combine like terms: 3.354101966 + 2 = 5.354101966 x = 5.354101966 Simplifying x = 5.354101966Subproblem 2
x + -2 = -3.354101966 Simplifying x + -2 = -3.354101966 Reorder the terms: -2 + x = -3.354101966 Solving -2 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.354101966 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.354101966 + 2 x = -3.354101966 + 2 Combine like terms: -3.354101966 + 2 = -1.354101966 x = -1.354101966 Simplifying x = -1.354101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.354101966, -1.354101966}Solution
x = {5.354101966, -1.354101966}
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