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Simplifying 132 + 5x + -0.83x2 = 0 Solving 132 + 5x + -0.83x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.83 the coefficient of the squared term: Divide each side by '-0.83'. -159.0361446 + -6.024096386x + x2 = 0 Move the constant term to the right: Add '159.0361446' to each side of the equation. -159.0361446 + -6.024096386x + 159.0361446 + x2 = 0 + 159.0361446 Reorder the terms: -159.0361446 + 159.0361446 + -6.024096386x + x2 = 0 + 159.0361446 Combine like terms: -159.0361446 + 159.0361446 = 0.0000000 0.0000000 + -6.024096386x + x2 = 0 + 159.0361446 -6.024096386x + x2 = 0 + 159.0361446 Combine like terms: 0 + 159.0361446 = 159.0361446 -6.024096386x + x2 = 159.0361446 The x term is -6.024096386x. Take half its coefficient (-3.012048193). Square it (9.072434317) and add it to both sides. Add '9.072434317' to each side of the equation. -6.024096386x + 9.072434317 + x2 = 159.0361446 + 9.072434317 Reorder the terms: 9.072434317 + -6.024096386x + x2 = 159.0361446 + 9.072434317 Combine like terms: 159.0361446 + 9.072434317 = 168.108578917 9.072434317 + -6.024096386x + x2 = 168.108578917 Factor a perfect square on the left side: (x + -3.012048193)(x + -3.012048193) = 168.108578917 Calculate the square root of the right side: 12.965669243 Break this problem into two subproblems by setting (x + -3.012048193) equal to 12.965669243 and -12.965669243.Subproblem 1
x + -3.012048193 = 12.965669243 Simplifying x + -3.012048193 = 12.965669243 Reorder the terms: -3.012048193 + x = 12.965669243 Solving -3.012048193 + x = 12.965669243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.012048193' to each side of the equation. -3.012048193 + 3.012048193 + x = 12.965669243 + 3.012048193 Combine like terms: -3.012048193 + 3.012048193 = 0.000000000 0.000000000 + x = 12.965669243 + 3.012048193 x = 12.965669243 + 3.012048193 Combine like terms: 12.965669243 + 3.012048193 = 15.977717436 x = 15.977717436 Simplifying x = 15.977717436Subproblem 2
x + -3.012048193 = -12.965669243 Simplifying x + -3.012048193 = -12.965669243 Reorder the terms: -3.012048193 + x = -12.965669243 Solving -3.012048193 + x = -12.965669243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.012048193' to each side of the equation. -3.012048193 + 3.012048193 + x = -12.965669243 + 3.012048193 Combine like terms: -3.012048193 + 3.012048193 = 0.000000000 0.000000000 + x = -12.965669243 + 3.012048193 x = -12.965669243 + 3.012048193 Combine like terms: -12.965669243 + 3.012048193 = -9.95362105 x = -9.95362105 Simplifying x = -9.95362105Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.977717436, -9.95362105}
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