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Simplifying -5(s + 12) * 3s = -64 Reorder the terms: -5(12 + s) * 3s = -64 Reorder the terms for easier multiplication: -5 * 3s(12 + s) = -64 Multiply -5 * 3 -15s(12 + s) = -64 (12 * -15s + s * -15s) = -64 (-180s + -15s2) = -64 Solving -180s + -15s2 = -64 Solving for variable 's'. Reorder the terms: 64 + -180s + -15s2 = -64 + 64 Combine like terms: -64 + 64 = 0 64 + -180s + -15s2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -4.266666667 + 12s + s2 = 0 Move the constant term to the right: Add '4.266666667' to each side of the equation. -4.266666667 + 12s + 4.266666667 + s2 = 0 + 4.266666667 Reorder the terms: -4.266666667 + 4.266666667 + 12s + s2 = 0 + 4.266666667 Combine like terms: -4.266666667 + 4.266666667 = 0.000000000 0.000000000 + 12s + s2 = 0 + 4.266666667 12s + s2 = 0 + 4.266666667 Combine like terms: 0 + 4.266666667 = 4.266666667 12s + s2 = 4.266666667 The s term is 12s. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12s + 36 + s2 = 4.266666667 + 36 Reorder the terms: 36 + 12s + s2 = 4.266666667 + 36 Combine like terms: 4.266666667 + 36 = 40.266666667 36 + 12s + s2 = 40.266666667 Factor a perfect square on the left side: (s + 6)(s + 6) = 40.266666667 Calculate the square root of the right side: 6.345602152 Break this problem into two subproblems by setting (s + 6) equal to 6.345602152 and -6.345602152.Subproblem 1
s + 6 = 6.345602152 Simplifying s + 6 = 6.345602152 Reorder the terms: 6 + s = 6.345602152 Solving 6 + s = 6.345602152 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = 6.345602152 + -6 Combine like terms: 6 + -6 = 0 0 + s = 6.345602152 + -6 s = 6.345602152 + -6 Combine like terms: 6.345602152 + -6 = 0.345602152 s = 0.345602152 Simplifying s = 0.345602152Subproblem 2
s + 6 = -6.345602152 Simplifying s + 6 = -6.345602152 Reorder the terms: 6 + s = -6.345602152 Solving 6 + s = -6.345602152 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = -6.345602152 + -6 Combine like terms: 6 + -6 = 0 0 + s = -6.345602152 + -6 s = -6.345602152 + -6 Combine like terms: -6.345602152 + -6 = -12.345602152 s = -12.345602152 Simplifying s = -12.345602152Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.345602152, -12.345602152}
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