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Simplifying 0.52x2 + 4x + -177 = 0 Reorder the terms: -177 + 4x + 0.52x2 = 0 Solving -177 + 4x + 0.52x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.52 the coefficient of the squared term: Divide each side by '0.52'. -340.3846154 + 7.692307692x + x2 = 0 Move the constant term to the right: Add '340.3846154' to each side of the equation. -340.3846154 + 7.692307692x + 340.3846154 + x2 = 0 + 340.3846154 Reorder the terms: -340.3846154 + 340.3846154 + 7.692307692x + x2 = 0 + 340.3846154 Combine like terms: -340.3846154 + 340.3846154 = 0.0000000 0.0000000 + 7.692307692x + x2 = 0 + 340.3846154 7.692307692x + x2 = 0 + 340.3846154 Combine like terms: 0 + 340.3846154 = 340.3846154 7.692307692x + x2 = 340.3846154 The x term is 7.692307692x. Take half its coefficient (3.846153846). Square it (14.79289941) and add it to both sides. Add '14.79289941' to each side of the equation. 7.692307692x + 14.79289941 + x2 = 340.3846154 + 14.79289941 Reorder the terms: 14.79289941 + 7.692307692x + x2 = 340.3846154 + 14.79289941 Combine like terms: 340.3846154 + 14.79289941 = 355.17751481 14.79289941 + 7.692307692x + x2 = 355.17751481 Factor a perfect square on the left side: (x + 3.846153846)(x + 3.846153846) = 355.17751481 Calculate the square root of the right side: 18.846153847 Break this problem into two subproblems by setting (x + 3.846153846) equal to 18.846153847 and -18.846153847.Subproblem 1
x + 3.846153846 = 18.846153847 Simplifying x + 3.846153846 = 18.846153847 Reorder the terms: 3.846153846 + x = 18.846153847 Solving 3.846153846 + x = 18.846153847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.846153846' to each side of the equation. 3.846153846 + -3.846153846 + x = 18.846153847 + -3.846153846 Combine like terms: 3.846153846 + -3.846153846 = 0.000000000 0.000000000 + x = 18.846153847 + -3.846153846 x = 18.846153847 + -3.846153846 Combine like terms: 18.846153847 + -3.846153846 = 15.000000001 x = 15.000000001 Simplifying x = 15.000000001Subproblem 2
x + 3.846153846 = -18.846153847 Simplifying x + 3.846153846 = -18.846153847 Reorder the terms: 3.846153846 + x = -18.846153847 Solving 3.846153846 + x = -18.846153847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.846153846' to each side of the equation. 3.846153846 + -3.846153846 + x = -18.846153847 + -3.846153846 Combine like terms: 3.846153846 + -3.846153846 = 0.000000000 0.000000000 + x = -18.846153847 + -3.846153846 x = -18.846153847 + -3.846153846 Combine like terms: -18.846153847 + -3.846153846 = -22.692307693 x = -22.692307693 Simplifying x = -22.692307693Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.000000001, -22.692307693}
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