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Simplifying -16x2 + 128x + 240 = 0 Reorder the terms: 240 + 128x + -16x2 = 0 Solving 240 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(15 + 8x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(15 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + 8x + -1x2 = 0 Solving 15 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -8x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -8x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -8x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8x + x2 = 0 + 15 -8x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8x + x2 = 15 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 15 + 16 Reorder the terms: 16 + -8x + x2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + -8x + x2 = 31 Factor a perfect square on the left side: (x + -4)(x + -4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -4) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -4 = 5.567764363 Simplifying x + -4 = 5.567764363 Reorder the terms: -4 + x = 5.567764363 Solving -4 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.567764363 + 4 x = 5.567764363 + 4 Combine like terms: 5.567764363 + 4 = 9.567764363 x = 9.567764363 Simplifying x = 9.567764363Subproblem 2
x + -4 = -5.567764363 Simplifying x + -4 = -5.567764363 Reorder the terms: -4 + x = -5.567764363 Solving -4 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.567764363 + 4 x = -5.567764363 + 4 Combine like terms: -5.567764363 + 4 = -1.567764363 x = -1.567764363 Simplifying x = -1.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.567764363, -1.567764363}Solution
x = {9.567764363, -1.567764363}
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