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Simplifying -2.5(2s + -5) + -3(4.5s + -5.2) * s = 0 Reorder the terms: -2.5(-5 + 2s) + -3(4.5s + -5.2) * s = 0 (-5 * -2.5 + 2s * -2.5) + -3(4.5s + -5.2) * s = 0 (12.5 + -5s) + -3(4.5s + -5.2) * s = 0 Reorder the terms: 12.5 + -5s + -3(-5.2 + 4.5s) * s = 0 Reorder the terms for easier multiplication: 12.5 + -5s + -3s(-5.2 + 4.5s) = 0 12.5 + -5s + (-5.2 * -3s + 4.5s * -3s) = 0 12.5 + -5s + (15.6s + -13.5s2) = 0 Combine like terms: -5s + 15.6s = 10.6s 12.5 + 10.6s + -13.5s2 = 0 Solving 12.5 + 10.6s + -13.5s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -13.5 the coefficient of the squared term: Divide each side by '-13.5'. -0.9259259259 + -0.7851851852s + s2 = 0 Move the constant term to the right: Add '0.9259259259' to each side of the equation. -0.9259259259 + -0.7851851852s + 0.9259259259 + s2 = 0 + 0.9259259259 Reorder the terms: -0.9259259259 + 0.9259259259 + -0.7851851852s + s2 = 0 + 0.9259259259 Combine like terms: -0.9259259259 + 0.9259259259 = 0.0000000000 0.0000000000 + -0.7851851852s + s2 = 0 + 0.9259259259 -0.7851851852s + s2 = 0 + 0.9259259259 Combine like terms: 0 + 0.9259259259 = 0.9259259259 -0.7851851852s + s2 = 0.9259259259 The s term is -0.7851851852s. Take half its coefficient (-0.3925925926). Square it (0.1541289438) and add it to both sides. Add '0.1541289438' to each side of the equation. -0.7851851852s + 0.1541289438 + s2 = 0.9259259259 + 0.1541289438 Reorder the terms: 0.1541289438 + -0.7851851852s + s2 = 0.9259259259 + 0.1541289438 Combine like terms: 0.9259259259 + 0.1541289438 = 1.0800548697 0.1541289438 + -0.7851851852s + s2 = 1.0800548697 Factor a perfect square on the left side: (s + -0.3925925926)(s + -0.3925925926) = 1.0800548697 Calculate the square root of the right side: 1.039256883 Break this problem into two subproblems by setting (s + -0.3925925926) equal to 1.039256883 and -1.039256883.Subproblem 1
s + -0.3925925926 = 1.039256883 Simplifying s + -0.3925925926 = 1.039256883 Reorder the terms: -0.3925925926 + s = 1.039256883 Solving -0.3925925926 + s = 1.039256883 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3925925926' to each side of the equation. -0.3925925926 + 0.3925925926 + s = 1.039256883 + 0.3925925926 Combine like terms: -0.3925925926 + 0.3925925926 = 0.0000000000 0.0000000000 + s = 1.039256883 + 0.3925925926 s = 1.039256883 + 0.3925925926 Combine like terms: 1.039256883 + 0.3925925926 = 1.4318494756 s = 1.4318494756 Simplifying s = 1.4318494756Subproblem 2
s + -0.3925925926 = -1.039256883 Simplifying s + -0.3925925926 = -1.039256883 Reorder the terms: -0.3925925926 + s = -1.039256883 Solving -0.3925925926 + s = -1.039256883 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.3925925926' to each side of the equation. -0.3925925926 + 0.3925925926 + s = -1.039256883 + 0.3925925926 Combine like terms: -0.3925925926 + 0.3925925926 = 0.0000000000 0.0000000000 + s = -1.039256883 + 0.3925925926 s = -1.039256883 + 0.3925925926 Combine like terms: -1.039256883 + 0.3925925926 = -0.6466642904 s = -0.6466642904 Simplifying s = -0.6466642904Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.4318494756, -0.6466642904}
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