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Simplifying 3s2 + 4s + -4 = 8 Reorder the terms: -4 + 4s + 3s2 = 8 Solving -4 + 4s + 3s2 = 8 Solving for variable 's'. Reorder the terms: -4 + -8 + 4s + 3s2 = 8 + -8 Combine like terms: -4 + -8 = -12 -12 + 4s + 3s2 = 8 + -8 Combine like terms: 8 + -8 = 0 -12 + 4s + 3s2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 1.333333333s + s2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.333333333s + 4 + s2 = 0 + 4 Reorder the terms: -4 + 4 + 1.333333333s + s2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.333333333s + s2 = 0 + 4 1.333333333s + s2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.333333333s + s2 = 4 The s term is 1.333333333s. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333s + 0.4444444442 + s2 = 4 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333s + s2 = 4 + 0.4444444442 Combine like terms: 4 + 0.4444444442 = 4.4444444442 0.4444444442 + 1.333333333s + s2 = 4.4444444442 Factor a perfect square on the left side: (s + 0.6666666665)(s + 0.6666666665) = 4.4444444442 Calculate the square root of the right side: 2.108185107 Break this problem into two subproblems by setting (s + 0.6666666665) equal to 2.108185107 and -2.108185107.Subproblem 1
s + 0.6666666665 = 2.108185107 Simplifying s + 0.6666666665 = 2.108185107 Reorder the terms: 0.6666666665 + s = 2.108185107 Solving 0.6666666665 + s = 2.108185107 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + s = 2.108185107 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + s = 2.108185107 + -0.6666666665 s = 2.108185107 + -0.6666666665 Combine like terms: 2.108185107 + -0.6666666665 = 1.4415184405 s = 1.4415184405 Simplifying s = 1.4415184405Subproblem 2
s + 0.6666666665 = -2.108185107 Simplifying s + 0.6666666665 = -2.108185107 Reorder the terms: 0.6666666665 + s = -2.108185107 Solving 0.6666666665 + s = -2.108185107 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + s = -2.108185107 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + s = -2.108185107 + -0.6666666665 s = -2.108185107 + -0.6666666665 Combine like terms: -2.108185107 + -0.6666666665 = -2.7748517735 s = -2.7748517735 Simplifying s = -2.7748517735Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.4415184405, -2.7748517735}
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