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Simplifying 2x(x + 5) = 17 + -3x Reorder the terms: 2x(5 + x) = 17 + -3x (5 * 2x + x * 2x) = 17 + -3x (10x + 2x2) = 17 + -3x Solving 10x + 2x2 = 17 + -3x Solving for variable 'x'. Reorder the terms: -17 + 10x + 3x + 2x2 = 17 + -3x + -17 + 3x Combine like terms: 10x + 3x = 13x -17 + 13x + 2x2 = 17 + -3x + -17 + 3x Reorder the terms: -17 + 13x + 2x2 = 17 + -17 + -3x + 3x Combine like terms: 17 + -17 = 0 -17 + 13x + 2x2 = 0 + -3x + 3x -17 + 13x + 2x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -17 + 13x + 2x2 = 0 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 = 1.116062299 x = 1.116062299 Simplifying x = 1.116062299Subproblem 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 = -7.616062299 x = -7.616062299 Simplifying x = -7.616062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.116062299, -7.616062299}
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