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Simplifying 27.5x2 + -774.2x + -11613 = 0 Reorder the terms: -11613 + -774.2x + 27.5x2 = 0 Solving -11613 + -774.2x + 27.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27.5 the coefficient of the squared term: Divide each side by '27.5'. -422.2909091 + -28.15272727x + x2 = 0 Move the constant term to the right: Add '422.2909091' to each side of the equation. -422.2909091 + -28.15272727x + 422.2909091 + x2 = 0 + 422.2909091 Reorder the terms: -422.2909091 + 422.2909091 + -28.15272727x + x2 = 0 + 422.2909091 Combine like terms: -422.2909091 + 422.2909091 = 0.0000000 0.0000000 + -28.15272727x + x2 = 0 + 422.2909091 -28.15272727x + x2 = 0 + 422.2909091 Combine like terms: 0 + 422.2909091 = 422.2909091 -28.15272727x + x2 = 422.2909091 The x term is -28.15272727x. Take half its coefficient (-14.07636364). Square it (198.1440133) and add it to both sides. Add '198.1440133' to each side of the equation. -28.15272727x + 198.1440133 + x2 = 422.2909091 + 198.1440133 Reorder the terms: 198.1440133 + -28.15272727x + x2 = 422.2909091 + 198.1440133 Combine like terms: 422.2909091 + 198.1440133 = 620.4349224 198.1440133 + -28.15272727x + x2 = 620.4349224 Factor a perfect square on the left side: (x + -14.07636364)(x + -14.07636364) = 620.4349224 Calculate the square root of the right side: 24.908531117 Break this problem into two subproblems by setting (x + -14.07636364) equal to 24.908531117 and -24.908531117.Subproblem 1
x + -14.07636364 = 24.908531117 Simplifying x + -14.07636364 = 24.908531117 Reorder the terms: -14.07636364 + x = 24.908531117 Solving -14.07636364 + x = 24.908531117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.07636364' to each side of the equation. -14.07636364 + 14.07636364 + x = 24.908531117 + 14.07636364 Combine like terms: -14.07636364 + 14.07636364 = 0.00000000 0.00000000 + x = 24.908531117 + 14.07636364 x = 24.908531117 + 14.07636364 Combine like terms: 24.908531117 + 14.07636364 = 38.984894757 x = 38.984894757 Simplifying x = 38.984894757Subproblem 2
x + -14.07636364 = -24.908531117 Simplifying x + -14.07636364 = -24.908531117 Reorder the terms: -14.07636364 + x = -24.908531117 Solving -14.07636364 + x = -24.908531117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.07636364' to each side of the equation. -14.07636364 + 14.07636364 + x = -24.908531117 + 14.07636364 Combine like terms: -14.07636364 + 14.07636364 = 0.00000000 0.00000000 + x = -24.908531117 + 14.07636364 x = -24.908531117 + 14.07636364 Combine like terms: -24.908531117 + 14.07636364 = -10.832167477 x = -10.832167477 Simplifying x = -10.832167477Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.984894757, -10.832167477}
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