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Simplifying 8x2 + -13x + -20 = 0 Reorder the terms: -20 + -13x + 8x2 = 0 Solving -20 + -13x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.5 + -1.625x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.625x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.625x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.625x + x2 = 0 + 2.5 -1.625x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.625x + x2 = 2.5 The x term is -1.625x. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625x + 0.66015625 + x2 = 2.5 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = 2.5 + 0.66015625 Combine like terms: 2.5 + 0.66015625 = 3.16015625 0.66015625 + -1.625x + x2 = 3.16015625 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 3.16015625 Calculate the square root of the right side: 1.777682832 Break this problem into two subproblems by setting (x + -0.8125) equal to 1.777682832 and -1.777682832.Subproblem 1
x + -0.8125 = 1.777682832 Simplifying x + -0.8125 = 1.777682832 Reorder the terms: -0.8125 + x = 1.777682832 Solving -0.8125 + x = 1.777682832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 1.777682832 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 1.777682832 + 0.8125 x = 1.777682832 + 0.8125 Combine like terms: 1.777682832 + 0.8125 = 2.590182832 x = 2.590182832 Simplifying x = 2.590182832Subproblem 2
x + -0.8125 = -1.777682832 Simplifying x + -0.8125 = -1.777682832 Reorder the terms: -0.8125 + x = -1.777682832 Solving -0.8125 + x = -1.777682832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -1.777682832 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -1.777682832 + 0.8125 x = -1.777682832 + 0.8125 Combine like terms: -1.777682832 + 0.8125 = -0.965182832 x = -0.965182832 Simplifying x = -0.965182832Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.590182832, -0.965182832}
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