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Simplifying 660x2 + 529x + 85 = 0 Reorder the terms: 85 + 529x + 660x2 = 0 Solving 85 + 529x + 660x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 660 the coefficient of the squared term: Divide each side by '660'. 0.1287878788 + 0.8015151515x + x2 = 0 Move the constant term to the right: Add '-0.1287878788' to each side of the equation. 0.1287878788 + 0.8015151515x + -0.1287878788 + x2 = 0 + -0.1287878788 Reorder the terms: 0.1287878788 + -0.1287878788 + 0.8015151515x + x2 = 0 + -0.1287878788 Combine like terms: 0.1287878788 + -0.1287878788 = 0.0000000000 0.0000000000 + 0.8015151515x + x2 = 0 + -0.1287878788 0.8015151515x + x2 = 0 + -0.1287878788 Combine like terms: 0 + -0.1287878788 = -0.1287878788 0.8015151515x + x2 = -0.1287878788 The x term is 0.8015151515x. Take half its coefficient (0.4007575758). Square it (0.1606066346) and add it to both sides. Add '0.1606066346' to each side of the equation. 0.8015151515x + 0.1606066346 + x2 = -0.1287878788 + 0.1606066346 Reorder the terms: 0.1606066346 + 0.8015151515x + x2 = -0.1287878788 + 0.1606066346 Combine like terms: -0.1287878788 + 0.1606066346 = 0.0318187558 0.1606066346 + 0.8015151515x + x2 = 0.0318187558 Factor a perfect square on the left side: (x + 0.4007575758)(x + 0.4007575758) = 0.0318187558 Calculate the square root of the right side: 0.178378126 Break this problem into two subproblems by setting (x + 0.4007575758) equal to 0.178378126 and -0.178378126.Subproblem 1
x + 0.4007575758 = 0.178378126 Simplifying x + 0.4007575758 = 0.178378126 Reorder the terms: 0.4007575758 + x = 0.178378126 Solving 0.4007575758 + x = 0.178378126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4007575758' to each side of the equation. 0.4007575758 + -0.4007575758 + x = 0.178378126 + -0.4007575758 Combine like terms: 0.4007575758 + -0.4007575758 = 0.0000000000 0.0000000000 + x = 0.178378126 + -0.4007575758 x = 0.178378126 + -0.4007575758 Combine like terms: 0.178378126 + -0.4007575758 = -0.2223794498 x = -0.2223794498 Simplifying x = -0.2223794498Subproblem 2
x + 0.4007575758 = -0.178378126 Simplifying x + 0.4007575758 = -0.178378126 Reorder the terms: 0.4007575758 + x = -0.178378126 Solving 0.4007575758 + x = -0.178378126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4007575758' to each side of the equation. 0.4007575758 + -0.4007575758 + x = -0.178378126 + -0.4007575758 Combine like terms: 0.4007575758 + -0.4007575758 = 0.0000000000 0.0000000000 + x = -0.178378126 + -0.4007575758 x = -0.178378126 + -0.4007575758 Combine like terms: -0.178378126 + -0.4007575758 = -0.5791357018 x = -0.5791357018 Simplifying x = -0.5791357018Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2223794498, -0.5791357018}
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