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Simplifying 0 = -16x2 + 64x + 6 Reorder the terms: 0 = 6 + 64x + -16x2 Solving 0 = 6 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -64x + 16x2 = 6 + 64x + -16x2 + -6 + -64x + 16x2 Reorder the terms: -6 + -64x + 16x2 = 6 + -6 + 64x + -64x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -6 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -6 + -64x + 16x2 = 0 + -16x2 + 16x2 -6 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -32x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -32x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -32x + 8x2 = 0 Solving -3 + -32x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -4x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -4x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -4x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -4x + x2 = 0 + 0.375 -4x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -4x + x2 = 0.375 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 = 0.375 + 4 Reorder the terms: 4 + -4x + x2 = 0.375 + 4 Combine like terms: 0.375 + 4 = 4.375 4 + -4x + x2 = 4.375 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.375 Calculate the square root of the right side: 2.091650066 Break this problem into two subproblems by setting (x + -2) equal to 2.091650066 and -2.091650066.Subproblem 1
x + -2 = 2.091650066 Simplifying x + -2 = 2.091650066 Reorder the terms: -2 + x = 2.091650066 Solving -2 + x = 2.091650066 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 = 2.091650066 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.091650066 + 2 x = 2.091650066 + 2 Combine like terms: 2.091650066 + 2 = 4.091650066 x = 4.091650066 Simplifying x = 4.091650066Subproblem 2
x + -2 = -2.091650066 Simplifying x + -2 = -2.091650066 Reorder the terms: -2 + x = -2.091650066 Solving -2 + x = -2.091650066 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 = -2.091650066 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.091650066 + 2 x = -2.091650066 + 2 Combine like terms: -2.091650066 + 2 = -0.091650066 x = -0.091650066 Simplifying x = -0.091650066Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.091650066, -0.091650066}Solution
x = {4.091650066, -0.091650066}
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