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Simplifying -2x2 + 13x + 17 = 0 Reorder the terms: 17 + 13x + -2x2 = 0 Solving 17 + 13x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -6.5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -6.5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -6.5x + x2 = 0 + 8.5 -6.5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -6.5x + x2 = 8.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 8.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 8.5 + 10.5625 Combine like terms: 8.5 + 10.5625 = 19.0625 10.5625 + -6.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + -3.25) equal to 4.366062299 and -4.366062299.Subproblem 1
x + -3.25 = 4.366062299 Simplifying x + -3.25 = 4.366062299 Reorder the terms: -3.25 + x = 4.366062299 Solving -3.25 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.366062299 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.366062299 + 3.25 x = 4.366062299 + 3.25 Combine like terms: 4.366062299 + 3.25 = 7.616062299 x = 7.616062299 Simplifying x = 7.616062299Subproblem 2
x + -3.25 = -4.366062299 Simplifying x + -3.25 = -4.366062299 Reorder the terms: -3.25 + x = -4.366062299 Solving -3.25 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.366062299 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.366062299 + 3.25 x = -4.366062299 + 3.25 Combine like terms: -4.366062299 + 3.25 = -1.116062299 x = -1.116062299 Simplifying x = -1.116062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.616062299, -1.116062299}
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