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Simplifying (13x + 8) * 5x + -8 = 180 Reorder the terms: (8 + 13x) * 5x + -8 = 180 Reorder the terms for easier multiplication: 5x(8 + 13x) + -8 = 180 (8 * 5x + 13x * 5x) + -8 = 180 (40x + 65x2) + -8 = 180 Reorder the terms: -8 + 40x + 65x2 = 180 Solving -8 + 40x + 65x2 = 180 Solving for variable 'x'. Reorder the terms: -8 + -180 + 40x + 65x2 = 180 + -180 Combine like terms: -8 + -180 = -188 -188 + 40x + 65x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -188 + 40x + 65x2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. -2.892307692 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '2.892307692' to each side of the equation. -2.892307692 + 0.6153846154x + 2.892307692 + x2 = 0 + 2.892307692 Reorder the terms: -2.892307692 + 2.892307692 + 0.6153846154x + x2 = 0 + 2.892307692 Combine like terms: -2.892307692 + 2.892307692 = 0.000000000 0.000000000 + 0.6153846154x + x2 = 0 + 2.892307692 0.6153846154x + x2 = 0 + 2.892307692 Combine like terms: 0 + 2.892307692 = 2.892307692 0.6153846154x + x2 = 2.892307692 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 = 2.892307692 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 2.892307692 + 0.09467455622 Combine like terms: 2.892307692 + 0.09467455622 = 2.98698224822 0.09467455622 + 0.6153846154x + x2 = 2.98698224822 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 2.98698224822 Calculate the square root of the right side: 1.728288821 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 1.728288821 and -1.728288821.Subproblem 1
x + 0.3076923077 = 1.728288821 Simplifying x + 0.3076923077 = 1.728288821 Reorder the terms: 0.3076923077 + x = 1.728288821 Solving 0.3076923077 + x = 1.728288821 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 = 1.728288821 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 1.728288821 + -0.3076923077 x = 1.728288821 + -0.3076923077 Combine like terms: 1.728288821 + -0.3076923077 = 1.4205965133 x = 1.4205965133 Simplifying x = 1.4205965133Subproblem 2
x + 0.3076923077 = -1.728288821 Simplifying x + 0.3076923077 = -1.728288821 Reorder the terms: 0.3076923077 + x = -1.728288821 Solving 0.3076923077 + x = -1.728288821 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 = -1.728288821 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -1.728288821 + -0.3076923077 x = -1.728288821 + -0.3076923077 Combine like terms: -1.728288821 + -0.3076923077 = -2.0359811287 x = -2.0359811287 Simplifying x = -2.0359811287Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4205965133, -2.0359811287}
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