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Simplifying 3s2 + 12s + 8 = 0 Reorder the terms: 8 + 12s + 3s2 = 0 Solving 8 + 12s + 3s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 4s + s2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 4s + -2.666666667 + s2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 4s + s2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 4s + s2 = 0 + -2.666666667 4s + s2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 4s + s2 = -2.666666667 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = -2.666666667 + 4 Reorder the terms: 4 + 4s + s2 = -2.666666667 + 4 Combine like terms: -2.666666667 + 4 = 1.333333333 4 + 4s + s2 = 1.333333333 Factor a perfect square on the left side: (s + 2)(s + 2) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (s + 2) equal to 1.154700538 and -1.154700538.Subproblem 1
s + 2 = 1.154700538 Simplifying s + 2 = 1.154700538 Reorder the terms: 2 + s = 1.154700538 Solving 2 + s = 1.154700538 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 1.154700538 + -2 Combine like terms: 2 + -2 = 0 0 + s = 1.154700538 + -2 s = 1.154700538 + -2 Combine like terms: 1.154700538 + -2 = -0.845299462 s = -0.845299462 Simplifying s = -0.845299462Subproblem 2
s + 2 = -1.154700538 Simplifying s + 2 = -1.154700538 Reorder the terms: 2 + s = -1.154700538 Solving 2 + s = -1.154700538 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -1.154700538 + -2 Combine like terms: 2 + -2 = 0 0 + s = -1.154700538 + -2 s = -1.154700538 + -2 Combine like terms: -1.154700538 + -2 = -3.154700538 s = -3.154700538 Simplifying s = -3.154700538Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.845299462, -3.154700538}
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