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Simplifying -8s(-2s + -19) + 13 = 5s Reorder the terms: -8s(-19 + -2s) + 13 = 5s (-19 * -8s + -2s * -8s) + 13 = 5s (152s + 16s2) + 13 = 5s Reorder the terms: 13 + 152s + 16s2 = 5s Solving 13 + 152s + 16s2 = 5s Solving for variable 's'. Reorder the terms: 13 + 152s + -5s + 16s2 = 5s + -5s Combine like terms: 152s + -5s = 147s 13 + 147s + 16s2 = 5s + -5s Combine like terms: 5s + -5s = 0 13 + 147s + 16s2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.8125 + 9.1875s + s2 = 0 Move the constant term to the right: Add '-0.8125' to each side of the equation. 0.8125 + 9.1875s + -0.8125 + s2 = 0 + -0.8125 Reorder the terms: 0.8125 + -0.8125 + 9.1875s + s2 = 0 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + 9.1875s + s2 = 0 + -0.8125 9.1875s + s2 = 0 + -0.8125 Combine like terms: 0 + -0.8125 = -0.8125 9.1875s + s2 = -0.8125 The s term is 9.1875s. Take half its coefficient (4.59375). Square it (21.10253906) and add it to both sides. Add '21.10253906' to each side of the equation. 9.1875s + 21.10253906 + s2 = -0.8125 + 21.10253906 Reorder the terms: 21.10253906 + 9.1875s + s2 = -0.8125 + 21.10253906 Combine like terms: -0.8125 + 21.10253906 = 20.29003906 21.10253906 + 9.1875s + s2 = 20.29003906 Factor a perfect square on the left side: (s + 4.59375)(s + 4.59375) = 20.29003906 Calculate the square root of the right side: 4.504446588 Break this problem into two subproblems by setting (s + 4.59375) equal to 4.504446588 and -4.504446588.Subproblem 1
s + 4.59375 = 4.504446588 Simplifying s + 4.59375 = 4.504446588 Reorder the terms: 4.59375 + s = 4.504446588 Solving 4.59375 + s = 4.504446588 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.59375' to each side of the equation. 4.59375 + -4.59375 + s = 4.504446588 + -4.59375 Combine like terms: 4.59375 + -4.59375 = 0.00000 0.00000 + s = 4.504446588 + -4.59375 s = 4.504446588 + -4.59375 Combine like terms: 4.504446588 + -4.59375 = -0.089303412 s = -0.089303412 Simplifying s = -0.089303412Subproblem 2
s + 4.59375 = -4.504446588 Simplifying s + 4.59375 = -4.504446588 Reorder the terms: 4.59375 + s = -4.504446588 Solving 4.59375 + s = -4.504446588 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.59375' to each side of the equation. 4.59375 + -4.59375 + s = -4.504446588 + -4.59375 Combine like terms: 4.59375 + -4.59375 = 0.00000 0.00000 + s = -4.504446588 + -4.59375 s = -4.504446588 + -4.59375 Combine like terms: -4.504446588 + -4.59375 = -9.098196588 s = -9.098196588 Simplifying s = -9.098196588Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.089303412, -9.098196588}
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