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Simplifying -16x2 + 128x + 170 = 0 Reorder the terms: 170 + 128x + -16x2 = 0 Solving 170 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(85 + 64x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(85 + 64x + -8x2)' equal to zero and attempt to solve: Simplifying 85 + 64x + -8x2 = 0 Solving 85 + 64x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -10.625 + -8x + x2 = 0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + -8x + 10.625 + x2 = 0 + 10.625 Reorder the terms: -10.625 + 10.625 + -8x + x2 = 0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + -8x + x2 = 0 + 10.625 -8x + x2 = 0 + 10.625 Combine like terms: 0 + 10.625 = 10.625 -8x + x2 = 10.625 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 = 10.625 + 16 Reorder the terms: 16 + -8x + x2 = 10.625 + 16 Combine like terms: 10.625 + 16 = 26.625 16 + -8x + x2 = 26.625 Factor a perfect square on the left side: (x + -4)(x + -4) = 26.625 Calculate the square root of the right side: 5.15994186 Break this problem into two subproblems by setting (x + -4) equal to 5.15994186 and -5.15994186.Subproblem 1
x + -4 = 5.15994186 Simplifying x + -4 = 5.15994186 Reorder the terms: -4 + x = 5.15994186 Solving -4 + x = 5.15994186 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 = 5.15994186 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.15994186 + 4 x = 5.15994186 + 4 Combine like terms: 5.15994186 + 4 = 9.15994186 x = 9.15994186 Simplifying x = 9.15994186Subproblem 2
x + -4 = -5.15994186 Simplifying x + -4 = -5.15994186 Reorder the terms: -4 + x = -5.15994186 Solving -4 + x = -5.15994186 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 = -5.15994186 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.15994186 + 4 x = -5.15994186 + 4 Combine like terms: -5.15994186 + 4 = -1.15994186 x = -1.15994186 Simplifying x = -1.15994186Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.15994186, -1.15994186}Solution
x = {9.15994186, -1.15994186}
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