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Simplifying 3s(s + -2) = 125 Reorder the terms: 3s(-2 + s) = 125 (-2 * 3s + s * 3s) = 125 (-6s + 3s2) = 125 Solving -6s + 3s2 = 125 Solving for variable 's'. Reorder the terms: -125 + -6s + 3s2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -6s + 3s2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -41.66666667 + -2s + s2 = 0 Move the constant term to the right: Add '41.66666667' to each side of the equation. -41.66666667 + -2s + 41.66666667 + s2 = 0 + 41.66666667 Reorder the terms: -41.66666667 + 41.66666667 + -2s + s2 = 0 + 41.66666667 Combine like terms: -41.66666667 + 41.66666667 = 0.00000000 0.00000000 + -2s + s2 = 0 + 41.66666667 -2s + s2 = 0 + 41.66666667 Combine like terms: 0 + 41.66666667 = 41.66666667 -2s + s2 = 41.66666667 The s term is -2s. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2s + 1 + s2 = 41.66666667 + 1 Reorder the terms: 1 + -2s + s2 = 41.66666667 + 1 Combine like terms: 41.66666667 + 1 = 42.66666667 1 + -2s + s2 = 42.66666667 Factor a perfect square on the left side: (s + -1)(s + -1) = 42.66666667 Calculate the square root of the right side: 6.531972648 Break this problem into two subproblems by setting (s + -1) equal to 6.531972648 and -6.531972648.Subproblem 1
s + -1 = 6.531972648 Simplifying s + -1 = 6.531972648 Reorder the terms: -1 + s = 6.531972648 Solving -1 + s = 6.531972648 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 6.531972648 + 1 Combine like terms: -1 + 1 = 0 0 + s = 6.531972648 + 1 s = 6.531972648 + 1 Combine like terms: 6.531972648 + 1 = 7.531972648 s = 7.531972648 Simplifying s = 7.531972648Subproblem 2
s + -1 = -6.531972648 Simplifying s + -1 = -6.531972648 Reorder the terms: -1 + s = -6.531972648 Solving -1 + s = -6.531972648 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = -6.531972648 + 1 Combine like terms: -1 + 1 = 0 0 + s = -6.531972648 + 1 s = -6.531972648 + 1 Combine like terms: -6.531972648 + 1 = -5.531972648 s = -5.531972648 Simplifying s = -5.531972648Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.531972648, -5.531972648}
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