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Simplifying -16x2 + 64x + 128 = 0 Reorder the terms: 128 + 64x + -16x2 = 0 Solving 128 + 64x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(8 + 4x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(8 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 8 + 4x + -1x2 = 0 Solving 8 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -4x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -4x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -4x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4x + x2 = 0 + 8 -4x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4x + x2 = 8 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 = 8 + 4 Reorder the terms: 4 + -4x + x2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4x + x2 = 12 Factor a perfect square on the left side: (x + -2)(x + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -2 = 3.464101615 Simplifying x + -2 = 3.464101615 Reorder the terms: -2 + x = 3.464101615 Solving -2 + x = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.464101615 + 2 x = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 x = 5.464101615 Simplifying x = 5.464101615Subproblem 2
x + -2 = -3.464101615 Simplifying x + -2 = -3.464101615 Reorder the terms: -2 + x = -3.464101615 Solving -2 + x = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.464101615 + 2 x = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 x = -1.464101615 Simplifying x = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.464101615, -1.464101615}Solution
x = {5.464101615, -1.464101615}
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