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Simplifying 11x2 + -20x + 8 = 0 Reorder the terms: 8 + -20x + 11x2 = 0 Solving 8 + -20x + 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'. 0.7272727273 + -1.818181818x + x2 = 0 Move the constant term to the right: Add '-0.7272727273' to each side of the equation. 0.7272727273 + -1.818181818x + -0.7272727273 + x2 = 0 + -0.7272727273 Reorder the terms: 0.7272727273 + -0.7272727273 + -1.818181818x + x2 = 0 + -0.7272727273 Combine like terms: 0.7272727273 + -0.7272727273 = 0.0000000000 0.0000000000 + -1.818181818x + x2 = 0 + -0.7272727273 -1.818181818x + x2 = 0 + -0.7272727273 Combine like terms: 0 + -0.7272727273 = -0.7272727273 -1.818181818x + x2 = -0.7272727273 The x term is -1.818181818x. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818x + 0.8264462808 + x2 = -0.7272727273 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818x + x2 = -0.7272727273 + 0.8264462808 Combine like terms: -0.7272727273 + 0.8264462808 = 0.0991735535 0.8264462808 + -1.818181818x + x2 = 0.0991735535 Factor a perfect square on the left side: (x + -0.909090909)(x + -0.909090909) = 0.0991735535 Calculate the square root of the right side: 0.314918328 Break this problem into two subproblems by setting (x + -0.909090909) equal to 0.314918328 and -0.314918328.Subproblem 1
x + -0.909090909 = 0.314918328 Simplifying x + -0.909090909 = 0.314918328 Reorder the terms: -0.909090909 + x = 0.314918328 Solving -0.909090909 + x = 0.314918328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + x = 0.314918328 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + x = 0.314918328 + 0.909090909 x = 0.314918328 + 0.909090909 Combine like terms: 0.314918328 + 0.909090909 = 1.224009237 x = 1.224009237 Simplifying x = 1.224009237Subproblem 2
x + -0.909090909 = -0.314918328 Simplifying x + -0.909090909 = -0.314918328 Reorder the terms: -0.909090909 + x = -0.314918328 Solving -0.909090909 + x = -0.314918328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + x = -0.314918328 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + x = -0.314918328 + 0.909090909 x = -0.314918328 + 0.909090909 Combine like terms: -0.314918328 + 0.909090909 = 0.594172581 x = 0.594172581 Simplifying x = 0.594172581Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.224009237, 0.594172581}
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