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Simplifying 13x2 + 8x + -399 = 0 Reorder the terms: -399 + 8x + 13x2 = 0 Solving -399 + 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'. -30.69230769 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '30.69230769' to each side of the equation. -30.69230769 + 0.6153846154x + 30.69230769 + x2 = 0 + 30.69230769 Reorder the terms: -30.69230769 + 30.69230769 + 0.6153846154x + x2 = 0 + 30.69230769 Combine like terms: -30.69230769 + 30.69230769 = 0.00000000 0.00000000 + 0.6153846154x + x2 = 0 + 30.69230769 0.6153846154x + x2 = 0 + 30.69230769 Combine like terms: 0 + 30.69230769 = 30.69230769 0.6153846154x + x2 = 30.69230769 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 = 30.69230769 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 30.69230769 + 0.09467455622 Combine like terms: 30.69230769 + 0.09467455622 = 30.78698224622 0.09467455622 + 0.6153846154x + x2 = 30.78698224622 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 30.78698224622 Calculate the square root of the right side: 5.548601828 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 5.548601828 and -5.548601828.Subproblem 1
x + 0.3076923077 = 5.548601828 Simplifying x + 0.3076923077 = 5.548601828 Reorder the terms: 0.3076923077 + x = 5.548601828 Solving 0.3076923077 + x = 5.548601828 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 = 5.548601828 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 5.548601828 + -0.3076923077 x = 5.548601828 + -0.3076923077 Combine like terms: 5.548601828 + -0.3076923077 = 5.2409095203 x = 5.2409095203 Simplifying x = 5.2409095203Subproblem 2
x + 0.3076923077 = -5.548601828 Simplifying x + 0.3076923077 = -5.548601828 Reorder the terms: 0.3076923077 + x = -5.548601828 Solving 0.3076923077 + x = -5.548601828 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 = -5.548601828 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -5.548601828 + -0.3076923077 x = -5.548601828 + -0.3076923077 Combine like terms: -5.548601828 + -0.3076923077 = -5.8562941357 x = -5.8562941357 Simplifying x = -5.8562941357Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2409095203, -5.8562941357}
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