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Simplifying 2x2 + -23x + 54 = 0 Reorder the terms: 54 + -23x + 2x2 = 0 Solving 54 + -23x + 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'. 27 + -11.5x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -11.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -11.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -11.5x + x2 = 0 + -27 -11.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -11.5x + x2 = -27 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 = -27 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -27 + 33.0625 Combine like terms: -27 + 33.0625 = 6.0625 33.0625 + -11.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -5.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -5.75 = 2.46221445 Simplifying x + -5.75 = 2.46221445 Reorder the terms: -5.75 + x = 2.46221445 Solving -5.75 + x = 2.46221445 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 = 2.46221445 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 2.46221445 + 5.75 x = 2.46221445 + 5.75 Combine like terms: 2.46221445 + 5.75 = 8.21221445 x = 8.21221445 Simplifying x = 8.21221445Subproblem 2
x + -5.75 = -2.46221445 Simplifying x + -5.75 = -2.46221445 Reorder the terms: -5.75 + x = -2.46221445 Solving -5.75 + x = -2.46221445 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 = -2.46221445 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -2.46221445 + 5.75 x = -2.46221445 + 5.75 Combine like terms: -2.46221445 + 5.75 = 3.28778555 x = 3.28778555 Simplifying x = 3.28778555Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.21221445, 3.28778555}
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