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Simplifying 0.7(3s + 4) * 1.1s = 7.9 Reorder the terms: 0.7(4 + 3s) * 1.1s = 7.9 Reorder the terms for easier multiplication: 0.7 * 1.1s(4 + 3s) = 7.9 Multiply 0.7 * 1.1 0.77s(4 + 3s) = 7.9 (4 * 0.77s + 3s * 0.77s) = 7.9 (3.08s + 2.31s2) = 7.9 Solving 3.08s + 2.31s2 = 7.9 Solving for variable 's'. Reorder the terms: -7.9 + 3.08s + 2.31s2 = 7.9 + -7.9 Combine like terms: 7.9 + -7.9 = 0.0 -7.9 + 3.08s + 2.31s2 = 0.0 Begin completing the square. Divide all terms by 2.31 the coefficient of the squared term: Divide each side by '2.31'. -3.41991342 + 1.333333333s + s2 = 0 Move the constant term to the right: Add '3.41991342' to each side of the equation. -3.41991342 + 1.333333333s + 3.41991342 + s2 = 0 + 3.41991342 Reorder the terms: -3.41991342 + 3.41991342 + 1.333333333s + s2 = 0 + 3.41991342 Combine like terms: -3.41991342 + 3.41991342 = 0.00000000 0.00000000 + 1.333333333s + s2 = 0 + 3.41991342 1.333333333s + s2 = 0 + 3.41991342 Combine like terms: 0 + 3.41991342 = 3.41991342 1.333333333s + s2 = 3.41991342 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 = 3.41991342 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333s + s2 = 3.41991342 + 0.4444444442 Combine like terms: 3.41991342 + 0.4444444442 = 3.8643578642 0.4444444442 + 1.333333333s + s2 = 3.8643578642 Factor a perfect square on the left side: (s + 0.6666666665)(s + 0.6666666665) = 3.8643578642 Calculate the square root of the right side: 1.965797005 Break this problem into two subproblems by setting (s + 0.6666666665) equal to 1.965797005 and -1.965797005.Subproblem 1
s + 0.6666666665 = 1.965797005 Simplifying s + 0.6666666665 = 1.965797005 Reorder the terms: 0.6666666665 + s = 1.965797005 Solving 0.6666666665 + s = 1.965797005 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 = 1.965797005 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + s = 1.965797005 + -0.6666666665 s = 1.965797005 + -0.6666666665 Combine like terms: 1.965797005 + -0.6666666665 = 1.2991303385 s = 1.2991303385 Simplifying s = 1.2991303385Subproblem 2
s + 0.6666666665 = -1.965797005 Simplifying s + 0.6666666665 = -1.965797005 Reorder the terms: 0.6666666665 + s = -1.965797005 Solving 0.6666666665 + s = -1.965797005 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 = -1.965797005 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + s = -1.965797005 + -0.6666666665 s = -1.965797005 + -0.6666666665 Combine like terms: -1.965797005 + -0.6666666665 = -2.6324636715 s = -2.6324636715 Simplifying s = -2.6324636715Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.2991303385, -2.6324636715}
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