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Simplifying x2 + 34x + 90 = 0 Reorder the terms: 90 + 34x + x2 = 0 Solving 90 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + 34x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 34x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 34x + x2 = 0 + -90 34x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 34x + x2 = -90 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = -90 + 289 Reorder the terms: 289 + 34x + x2 = -90 + 289 Combine like terms: -90 + 289 = 199 289 + 34x + x2 = 199 Factor a perfect square on the left side: (x + 17)(x + 17) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (x + 17) equal to 14.10673598 and -14.10673598.Subproblem 1
x + 17 = 14.10673598 Simplifying x + 17 = 14.10673598 Reorder the terms: 17 + x = 14.10673598 Solving 17 + x = 14.10673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 14.10673598 + -17 Combine like terms: 17 + -17 = 0 0 + x = 14.10673598 + -17 x = 14.10673598 + -17 Combine like terms: 14.10673598 + -17 = -2.89326402 x = -2.89326402 Simplifying x = -2.89326402Subproblem 2
x + 17 = -14.10673598 Simplifying x + 17 = -14.10673598 Reorder the terms: 17 + x = -14.10673598 Solving 17 + x = -14.10673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -14.10673598 + -17 Combine like terms: 17 + -17 = 0 0 + x = -14.10673598 + -17 x = -14.10673598 + -17 Combine like terms: -14.10673598 + -17 = -31.10673598 x = -31.10673598 Simplifying x = -31.10673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.89326402, -31.10673598}
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