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Simplifying -2x2 + -5x + 27 = 0 Reorder the terms: 27 + -5x + -2x2 = 0 Solving 27 + -5x + -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'. -13.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 2.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 2.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 2.5x + x2 = 0 + 13.5 2.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 2.5x + x2 = 13.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 13.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 13.5 + 1.5625 Combine like terms: 13.5 + 1.5625 = 15.0625 1.5625 + 2.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 1.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 1.25 = 3.881043674 Simplifying x + 1.25 = 3.881043674 Reorder the terms: 1.25 + x = 3.881043674 Solving 1.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.881043674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.881043674 + -1.25 x = 3.881043674 + -1.25 Combine like terms: 3.881043674 + -1.25 = 2.631043674 x = 2.631043674 Simplifying x = 2.631043674Subproblem 2
x + 1.25 = -3.881043674 Simplifying x + 1.25 = -3.881043674 Reorder the terms: 1.25 + x = -3.881043674 Solving 1.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.881043674 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.881043674 + -1.25 x = -3.881043674 + -1.25 Combine like terms: -3.881043674 + -1.25 = -5.131043674 x = -5.131043674 Simplifying x = -5.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.631043674, -5.131043674}
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