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Simplifying 13x2 + 8x + -7 = 0 Reorder the terms: -7 + 8x + 13x2 = 0 Solving -7 + 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'. -0.5384615385 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.6153846154x + 0.5384615385 + x2 = 0 + 0.5384615385 Reorder the terms: -0.5384615385 + 0.5384615385 + 0.6153846154x + x2 = 0 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + 0.6153846154x + x2 = 0 + 0.5384615385 0.6153846154x + x2 = 0 + 0.5384615385 Combine like terms: 0 + 0.5384615385 = 0.5384615385 0.6153846154x + x2 = 0.5384615385 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 = 0.5384615385 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 0.5384615385 + 0.09467455622 Combine like terms: 0.5384615385 + 0.09467455622 = 0.63313609472 0.09467455622 + 0.6153846154x + x2 = 0.63313609472 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 0.63313609472 Calculate the square root of the right side: 0.795698495 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 0.795698495 and -0.795698495.Subproblem 1
x + 0.3076923077 = 0.795698495 Simplifying x + 0.3076923077 = 0.795698495 Reorder the terms: 0.3076923077 + x = 0.795698495 Solving 0.3076923077 + x = 0.795698495 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 = 0.795698495 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 0.795698495 + -0.3076923077 x = 0.795698495 + -0.3076923077 Combine like terms: 0.795698495 + -0.3076923077 = 0.4880061873 x = 0.4880061873 Simplifying x = 0.4880061873Subproblem 2
x + 0.3076923077 = -0.795698495 Simplifying x + 0.3076923077 = -0.795698495 Reorder the terms: 0.3076923077 + x = -0.795698495 Solving 0.3076923077 + x = -0.795698495 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 = -0.795698495 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -0.795698495 + -0.3076923077 x = -0.795698495 + -0.3076923077 Combine like terms: -0.795698495 + -0.3076923077 = -1.1033908027 x = -1.1033908027 Simplifying x = -1.1033908027Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4880061873, -1.1033908027}
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