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Simplifying x(20x + -131) = 66 Reorder the terms: x(-131 + 20x) = 66 (-131 * x + 20x * x) = 66 (-131x + 20x2) = 66 Solving -131x + 20x2 = 66 Solving for variable 'x'. Reorder the terms: -66 + -131x + 20x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + -131x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -3.3 + -6.55x + x2 = 0 Move the constant term to the right: Add '3.3' to each side of the equation. -3.3 + -6.55x + 3.3 + x2 = 0 + 3.3 Reorder the terms: -3.3 + 3.3 + -6.55x + x2 = 0 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + -6.55x + x2 = 0 + 3.3 -6.55x + x2 = 0 + 3.3 Combine like terms: 0 + 3.3 = 3.3 -6.55x + x2 = 3.3 The x term is -6.55x. Take half its coefficient (-3.275). Square it (10.725625) and add it to both sides. Add '10.725625' to each side of the equation. -6.55x + 10.725625 + x2 = 3.3 + 10.725625 Reorder the terms: 10.725625 + -6.55x + x2 = 3.3 + 10.725625 Combine like terms: 3.3 + 10.725625 = 14.025625 10.725625 + -6.55x + x2 = 14.025625 Factor a perfect square on the left side: (x + -3.275)(x + -3.275) = 14.025625 Calculate the square root of the right side: 3.745080106 Break this problem into two subproblems by setting (x + -3.275) equal to 3.745080106 and -3.745080106.Subproblem 1
x + -3.275 = 3.745080106 Simplifying x + -3.275 = 3.745080106 Reorder the terms: -3.275 + x = 3.745080106 Solving -3.275 + x = 3.745080106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.275' to each side of the equation. -3.275 + 3.275 + x = 3.745080106 + 3.275 Combine like terms: -3.275 + 3.275 = 0.000 0.000 + x = 3.745080106 + 3.275 x = 3.745080106 + 3.275 Combine like terms: 3.745080106 + 3.275 = 7.020080106 x = 7.020080106 Simplifying x = 7.020080106Subproblem 2
x + -3.275 = -3.745080106 Simplifying x + -3.275 = -3.745080106 Reorder the terms: -3.275 + x = -3.745080106 Solving -3.275 + x = -3.745080106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.275' to each side of the equation. -3.275 + 3.275 + x = -3.745080106 + 3.275 Combine like terms: -3.275 + 3.275 = 0.000 0.000 + x = -3.745080106 + 3.275 x = -3.745080106 + 3.275 Combine like terms: -3.745080106 + 3.275 = -0.470080106 x = -0.470080106 Simplifying x = -0.470080106Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.020080106, -0.470080106}
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