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Simplifying -1[2s(s + -9) + 3(s + 1) + -4] = 0 Reorder the terms: -1[2s(-9 + s) + 3(s + 1) + -4] = 0 -1[(-9 * 2s + s * 2s) + 3(s + 1) + -4] = 0 -1[(-18s + 2s2) + 3(s + 1) + -4] = 0 Reorder the terms: -1[-18s + 2s2 + 3(1 + s) + -4] = 0 -1[-18s + 2s2 + (1 * 3 + s * 3) + -4] = 0 -1[-18s + 2s2 + (3 + 3s) + -4] = 0 Reorder the terms: -1[3 + -4 + -18s + 3s + 2s2] = 0 Combine like terms: 3 + -4 = -1 -1[-1 + -18s + 3s + 2s2] = 0 Combine like terms: -18s + 3s = -15s -1[-1 + -15s + 2s2] = 0 [-1 * -1 + -15s * -1 + 2s2 * -1] = 0 [1 + 15s + -2s2] = 0 Solving 1 + 15s + -2s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -7.5s + s2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -7.5s + 0.5 + s2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -7.5s + s2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -7.5s + s2 = 0 + 0.5 -7.5s + s2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -7.5s + s2 = 0.5 The s term is -7.5s. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5s + 14.0625 + s2 = 0.5 + 14.0625 Reorder the terms: 14.0625 + -7.5s + s2 = 0.5 + 14.0625 Combine like terms: 0.5 + 14.0625 = 14.5625 14.0625 + -7.5s + s2 = 14.5625 Factor a perfect square on the left side: (s + -3.75)(s + -3.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (s + -3.75) equal to 3.816084381 and -3.816084381.Subproblem 1
s + -3.75 = 3.816084381 Simplifying s + -3.75 = 3.816084381 Reorder the terms: -3.75 + s = 3.816084381 Solving -3.75 + s = 3.816084381 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + s = 3.816084381 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + s = 3.816084381 + 3.75 s = 3.816084381 + 3.75 Combine like terms: 3.816084381 + 3.75 = 7.566084381 s = 7.566084381 Simplifying s = 7.566084381Subproblem 2
s + -3.75 = -3.816084381 Simplifying s + -3.75 = -3.816084381 Reorder the terms: -3.75 + s = -3.816084381 Solving -3.75 + s = -3.816084381 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + s = -3.816084381 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + s = -3.816084381 + 3.75 s = -3.816084381 + 3.75 Combine like terms: -3.816084381 + 3.75 = -0.066084381 s = -0.066084381 Simplifying s = -0.066084381Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.566084381, -0.066084381}
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