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Simplifying 7s2 + 112s + 64 = 0 Reorder the terms: 64 + 112s + 7s2 = 0 Solving 64 + 112s + 7s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 9.142857143 + 16s + s2 = 0 Move the constant term to the right: Add '-9.142857143' to each side of the equation. 9.142857143 + 16s + -9.142857143 + s2 = 0 + -9.142857143 Reorder the terms: 9.142857143 + -9.142857143 + 16s + s2 = 0 + -9.142857143 Combine like terms: 9.142857143 + -9.142857143 = 0.000000000 0.000000000 + 16s + s2 = 0 + -9.142857143 16s + s2 = 0 + -9.142857143 Combine like terms: 0 + -9.142857143 = -9.142857143 16s + s2 = -9.142857143 The s term is 16s. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16s + 64 + s2 = -9.142857143 + 64 Reorder the terms: 64 + 16s + s2 = -9.142857143 + 64 Combine like terms: -9.142857143 + 64 = 54.857142857 64 + 16s + s2 = 54.857142857 Factor a perfect square on the left side: (s + 8)(s + 8) = 54.857142857 Calculate the square root of the right side: 7.406560798 Break this problem into two subproblems by setting (s + 8) equal to 7.406560798 and -7.406560798.Subproblem 1
s + 8 = 7.406560798 Simplifying s + 8 = 7.406560798 Reorder the terms: 8 + s = 7.406560798 Solving 8 + s = 7.406560798 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = 7.406560798 + -8 Combine like terms: 8 + -8 = 0 0 + s = 7.406560798 + -8 s = 7.406560798 + -8 Combine like terms: 7.406560798 + -8 = -0.593439202 s = -0.593439202 Simplifying s = -0.593439202Subproblem 2
s + 8 = -7.406560798 Simplifying s + 8 = -7.406560798 Reorder the terms: 8 + s = -7.406560798 Solving 8 + s = -7.406560798 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = -7.406560798 + -8 Combine like terms: 8 + -8 = 0 0 + s = -7.406560798 + -8 s = -7.406560798 + -8 Combine like terms: -7.406560798 + -8 = -15.406560798 s = -15.406560798 Simplifying s = -15.406560798Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.593439202, -15.406560798}
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