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Simplifying 2x2 + -23x = 63 Reorder the terms: -23x + 2x2 = 63 Solving -23x + 2x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + -23x + 2x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + -11.5x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + -11.5x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + -11.5x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + -11.5x + x2 = 0 + 31.5 -11.5x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 -11.5x + x2 = 31.5 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 31.5 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 31.5 + 33.0625 Combine like terms: 31.5 + 33.0625 = 64.5625 33.0625 + -11.5x + x2 = 64.5625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 64.5625 Calculate the square root of the right side: 8.03507934 Break this problem into two subproblems by setting (x + -5.75) equal to 8.03507934 and -8.03507934.Subproblem 1
x + -5.75 = 8.03507934 Simplifying x + -5.75 = 8.03507934 Reorder the terms: -5.75 + x = 8.03507934 Solving -5.75 + x = 8.03507934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 8.03507934 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 8.03507934 + 5.75 x = 8.03507934 + 5.75 Combine like terms: 8.03507934 + 5.75 = 13.78507934 x = 13.78507934 Simplifying x = 13.78507934Subproblem 2
x + -5.75 = -8.03507934 Simplifying x + -5.75 = -8.03507934 Reorder the terms: -5.75 + x = -8.03507934 Solving -5.75 + x = -8.03507934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -8.03507934 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -8.03507934 + 5.75 x = -8.03507934 + 5.75 Combine like terms: -8.03507934 + 5.75 = -2.28507934 x = -2.28507934 Simplifying x = -2.28507934Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.78507934, -2.28507934}
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