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Simplifying 2x2 + 18x + 32 = (x + 5) Reorder the terms: 32 + 18x + 2x2 = (x + 5) Reorder the terms: 32 + 18x + 2x2 = (5 + x) Remove parenthesis around (5 + x) 32 + 18x + 2x2 = 5 + x Solving 32 + 18x + 2x2 = 5 + x Solving for variable 'x'. Reorder the terms: 32 + -5 + 18x + -1x + 2x2 = 5 + x + -5 + -1x Combine like terms: 32 + -5 = 27 27 + 18x + -1x + 2x2 = 5 + x + -5 + -1x Combine like terms: 18x + -1x = 17x 27 + 17x + 2x2 = 5 + x + -5 + -1x Reorder the terms: 27 + 17x + 2x2 = 5 + -5 + x + -1x Combine like terms: 5 + -5 = 0 27 + 17x + 2x2 = 0 + x + -1x 27 + 17x + 2x2 = x + -1x Combine like terms: x + -1x = 0 27 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 8.5x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 8.5x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 8.5x + x2 = 0 + -13.5 8.5x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 8.5x + x2 = -13.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -13.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -13.5 + 18.0625 Combine like terms: -13.5 + 18.0625 = 4.5625 18.0625 + 8.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 4.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 4.25 = 2.136000936 Simplifying x + 4.25 = 2.136000936 Reorder the terms: 4.25 + x = 2.136000936 Solving 4.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 2.136000936 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 2.136000936 + -4.25 x = 2.136000936 + -4.25 Combine like terms: 2.136000936 + -4.25 = -2.113999064 x = -2.113999064 Simplifying x = -2.113999064Subproblem 2
x + 4.25 = -2.136000936 Simplifying x + 4.25 = -2.136000936 Reorder the terms: 4.25 + x = -2.136000936 Solving 4.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -2.136000936 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -2.136000936 + -4.25 x = -2.136000936 + -4.25 Combine like terms: -2.136000936 + -4.25 = -6.386000936 x = -6.386000936 Simplifying x = -6.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.113999064, -6.386000936}
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