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Simplifying 11x2 + -234x + -7920 = 0 Reorder the terms: -7920 + -234x + 11x2 = 0 Solving -7920 + -234x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -720 + -21.27272727x + x2 = 0 Move the constant term to the right: Add '720' to each side of the equation. -720 + -21.27272727x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + -21.27272727x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + -21.27272727x + x2 = 0 + 720 -21.27272727x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 -21.27272727x + x2 = 720 The x term is -21.27272727x. Take half its coefficient (-10.63636364). Square it (113.1322315) and add it to both sides. Add '113.1322315' to each side of the equation. -21.27272727x + 113.1322315 + x2 = 720 + 113.1322315 Reorder the terms: 113.1322315 + -21.27272727x + x2 = 720 + 113.1322315 Combine like terms: 720 + 113.1322315 = 833.1322315 113.1322315 + -21.27272727x + x2 = 833.1322315 Factor a perfect square on the left side: (x + -10.63636364)(x + -10.63636364) = 833.1322315 Calculate the square root of the right side: 28.864030063 Break this problem into two subproblems by setting (x + -10.63636364) equal to 28.864030063 and -28.864030063.Subproblem 1
x + -10.63636364 = 28.864030063 Simplifying x + -10.63636364 = 28.864030063 Reorder the terms: -10.63636364 + x = 28.864030063 Solving -10.63636364 + x = 28.864030063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.63636364' to each side of the equation. -10.63636364 + 10.63636364 + x = 28.864030063 + 10.63636364 Combine like terms: -10.63636364 + 10.63636364 = 0.00000000 0.00000000 + x = 28.864030063 + 10.63636364 x = 28.864030063 + 10.63636364 Combine like terms: 28.864030063 + 10.63636364 = 39.500393703 x = 39.500393703 Simplifying x = 39.500393703Subproblem 2
x + -10.63636364 = -28.864030063 Simplifying x + -10.63636364 = -28.864030063 Reorder the terms: -10.63636364 + x = -28.864030063 Solving -10.63636364 + x = -28.864030063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.63636364' to each side of the equation. -10.63636364 + 10.63636364 + x = -28.864030063 + 10.63636364 Combine like terms: -10.63636364 + 10.63636364 = 0.00000000 0.00000000 + x = -28.864030063 + 10.63636364 x = -28.864030063 + 10.63636364 Combine like terms: -28.864030063 + 10.63636364 = -18.227666423 x = -18.227666423 Simplifying x = -18.227666423Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.500393703, -18.227666423}
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