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Simplifying 2x2 + -29x + 87 = 0 Reorder the terms: 87 + -29x + 2x2 = 0 Solving 87 + -29x + 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'. 43.5 + -14.5x + x2 = 0 Move the constant term to the right: Add '-43.5' to each side of the equation. 43.5 + -14.5x + -43.5 + x2 = 0 + -43.5 Reorder the terms: 43.5 + -43.5 + -14.5x + x2 = 0 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 0.0 + -14.5x + x2 = 0 + -43.5 -14.5x + x2 = 0 + -43.5 Combine like terms: 0 + -43.5 = -43.5 -14.5x + x2 = -43.5 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = -43.5 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = -43.5 + 52.5625 Combine like terms: -43.5 + 52.5625 = 9.0625 52.5625 + -14.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -7.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -7.25 = 3.010398645 Simplifying x + -7.25 = 3.010398645 Reorder the terms: -7.25 + x = 3.010398645 Solving -7.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 3.010398645 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 3.010398645 + 7.25 x = 3.010398645 + 7.25 Combine like terms: 3.010398645 + 7.25 = 10.260398645 x = 10.260398645 Simplifying x = 10.260398645Subproblem 2
x + -7.25 = -3.010398645 Simplifying x + -7.25 = -3.010398645 Reorder the terms: -7.25 + x = -3.010398645 Solving -7.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -3.010398645 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -3.010398645 + 7.25 x = -3.010398645 + 7.25 Combine like terms: -3.010398645 + 7.25 = 4.239601355 x = 4.239601355 Simplifying x = 4.239601355Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.260398645, 4.239601355}
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