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Simplifying 8x + 13x2 + -15 = 0 Reorder the terms: -15 + 8x + 13x2 = 0 Solving -15 + 8x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.153846154 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '1.153846154' to each side of the equation. -1.153846154 + 0.6153846154x + 1.153846154 + x2 = 0 + 1.153846154 Reorder the terms: -1.153846154 + 1.153846154 + 0.6153846154x + x2 = 0 + 1.153846154 Combine like terms: -1.153846154 + 1.153846154 = 0.000000000 0.000000000 + 0.6153846154x + x2 = 0 + 1.153846154 0.6153846154x + x2 = 0 + 1.153846154 Combine like terms: 0 + 1.153846154 = 1.153846154 0.6153846154x + x2 = 1.153846154 The x term is 0.6153846154x. Take half its coefficient (0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. 0.6153846154x + 0.09467455622 + x2 = 1.153846154 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 1.153846154 + 0.09467455622 Combine like terms: 1.153846154 + 0.09467455622 = 1.24852071022 0.09467455622 + 0.6153846154x + x2 = 1.24852071022 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 1.24852071022 Calculate the square root of the right side: 1.117372234 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 1.117372234 and -1.117372234.Subproblem 1
x + 0.3076923077 = 1.117372234 Simplifying x + 0.3076923077 = 1.117372234 Reorder the terms: 0.3076923077 + x = 1.117372234 Solving 0.3076923077 + x = 1.117372234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + x = 1.117372234 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 1.117372234 + -0.3076923077 x = 1.117372234 + -0.3076923077 Combine like terms: 1.117372234 + -0.3076923077 = 0.8096799263 x = 0.8096799263 Simplifying x = 0.8096799263Subproblem 2
x + 0.3076923077 = -1.117372234 Simplifying x + 0.3076923077 = -1.117372234 Reorder the terms: 0.3076923077 + x = -1.117372234 Solving 0.3076923077 + x = -1.117372234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + x = -1.117372234 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -1.117372234 + -0.3076923077 x = -1.117372234 + -0.3076923077 Combine like terms: -1.117372234 + -0.3076923077 = -1.4250645417 x = -1.4250645417 Simplifying x = -1.4250645417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8096799263, -1.4250645417}
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