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Simplifying 0 = 2x2 + 16x + -34 Reorder the terms: 0 = -34 + 16x + 2x2 Solving 0 = -34 + 16x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 34 = 34 34 + -16x + -2x2 = -34 + 16x + 2x2 + 34 + -16x + -2x2 Reorder the terms: 34 + -16x + -2x2 = -34 + 34 + 16x + -16x + 2x2 + -2x2 Combine like terms: -34 + 34 = 0 34 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2 34 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 34 + -16x + -2x2 = 0 + 2x2 + -2x2 34 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 34 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -8x + -1x2)' equal to zero and attempt to solve: Simplifying 17 + -8x + -1x2 = 0 Solving 17 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + 8x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 8x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 8x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 8x + x2 = 0 + 17 8x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 8x + x2 = 17 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 = 17 + 16 Reorder the terms: 16 + 8x + x2 = 17 + 16 Combine like terms: 17 + 16 = 33 16 + 8x + x2 = 33 Factor a perfect square on the left side: (x + 4)(x + 4) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 4) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 4 = 5.744562647 Simplifying x + 4 = 5.744562647 Reorder the terms: 4 + x = 5.744562647 Solving 4 + x = 5.744562647 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 = 5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.744562647 + -4 x = 5.744562647 + -4 Combine like terms: 5.744562647 + -4 = 1.744562647 x = 1.744562647 Simplifying x = 1.744562647Subproblem 2
x + 4 = -5.744562647 Simplifying x + 4 = -5.744562647 Reorder the terms: 4 + x = -5.744562647 Solving 4 + x = -5.744562647 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 = -5.744562647 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.744562647 + -4 x = -5.744562647 + -4 Combine like terms: -5.744562647 + -4 = -9.744562647 x = -9.744562647 Simplifying x = -9.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.744562647, -9.744562647}Solution
x = {1.744562647, -9.744562647}
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