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Simplifying -2x2 + 16x + 34 = 0 Reorder the terms: 34 + 16x + -2x2 = 0 Solving 34 + 16x + -2x2 = 0 Solving for variable 'x'. 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 = 9.744562647 x = 9.744562647 Simplifying x = 9.744562647Subproblem 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 = -1.744562647 x = -1.744562647 Simplifying x = -1.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.744562647, -1.744562647}Solution
x = {9.744562647, -1.744562647}
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