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Simplifying 56s2 + 23s + -64 = 0 Reorder the terms: -64 + 23s + 56s2 = 0 Solving -64 + 23s + 56s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -1.142857143 + 0.4107142857s + s2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 0.4107142857s + 1.142857143 + s2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 0.4107142857s + s2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 0.4107142857s + s2 = 0 + 1.142857143 0.4107142857s + s2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 0.4107142857s + s2 = 1.142857143 The s term is 0.4107142857s. Take half its coefficient (0.2053571429). Square it (0.04217155614) and add it to both sides. Add '0.04217155614' to each side of the equation. 0.4107142857s + 0.04217155614 + s2 = 1.142857143 + 0.04217155614 Reorder the terms: 0.04217155614 + 0.4107142857s + s2 = 1.142857143 + 0.04217155614 Combine like terms: 1.142857143 + 0.04217155614 = 1.18502869914 0.04217155614 + 0.4107142857s + s2 = 1.18502869914 Factor a perfect square on the left side: (s + 0.2053571429)(s + 0.2053571429) = 1.18502869914 Calculate the square root of the right side: 1.088590235 Break this problem into two subproblems by setting (s + 0.2053571429) equal to 1.088590235 and -1.088590235.Subproblem 1
s + 0.2053571429 = 1.088590235 Simplifying s + 0.2053571429 = 1.088590235 Reorder the terms: 0.2053571429 + s = 1.088590235 Solving 0.2053571429 + s = 1.088590235 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2053571429' to each side of the equation. 0.2053571429 + -0.2053571429 + s = 1.088590235 + -0.2053571429 Combine like terms: 0.2053571429 + -0.2053571429 = 0.0000000000 0.0000000000 + s = 1.088590235 + -0.2053571429 s = 1.088590235 + -0.2053571429 Combine like terms: 1.088590235 + -0.2053571429 = 0.8832330921 s = 0.8832330921 Simplifying s = 0.8832330921Subproblem 2
s + 0.2053571429 = -1.088590235 Simplifying s + 0.2053571429 = -1.088590235 Reorder the terms: 0.2053571429 + s = -1.088590235 Solving 0.2053571429 + s = -1.088590235 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.2053571429' to each side of the equation. 0.2053571429 + -0.2053571429 + s = -1.088590235 + -0.2053571429 Combine like terms: 0.2053571429 + -0.2053571429 = 0.0000000000 0.0000000000 + s = -1.088590235 + -0.2053571429 s = -1.088590235 + -0.2053571429 Combine like terms: -1.088590235 + -0.2053571429 = -1.2939473779 s = -1.2939473779 Simplifying s = -1.2939473779Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.8832330921, -1.2939473779}
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