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Simplifying 7s2 + 85s + 138 = 0 Reorder the terms: 138 + 85s + 7s2 = 0 Solving 138 + 85s + 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'. 19.71428571 + 12.14285714s + s2 = 0 Move the constant term to the right: Add '-19.71428571' to each side of the equation. 19.71428571 + 12.14285714s + -19.71428571 + s2 = 0 + -19.71428571 Reorder the terms: 19.71428571 + -19.71428571 + 12.14285714s + s2 = 0 + -19.71428571 Combine like terms: 19.71428571 + -19.71428571 = 0.00000000 0.00000000 + 12.14285714s + s2 = 0 + -19.71428571 12.14285714s + s2 = 0 + -19.71428571 Combine like terms: 0 + -19.71428571 = -19.71428571 12.14285714s + s2 = -19.71428571 The s term is 12.14285714s. Take half its coefficient (6.07142857). Square it (36.86224488) and add it to both sides. Add '36.86224488' to each side of the equation. 12.14285714s + 36.86224488 + s2 = -19.71428571 + 36.86224488 Reorder the terms: 36.86224488 + 12.14285714s + s2 = -19.71428571 + 36.86224488 Combine like terms: -19.71428571 + 36.86224488 = 17.14795917 36.86224488 + 12.14285714s + s2 = 17.14795917 Factor a perfect square on the left side: (s + 6.07142857)(s + 6.07142857) = 17.14795917 Calculate the square root of the right side: 4.141009439 Break this problem into two subproblems by setting (s + 6.07142857) equal to 4.141009439 and -4.141009439.Subproblem 1
s + 6.07142857 = 4.141009439 Simplifying s + 6.07142857 = 4.141009439 Reorder the terms: 6.07142857 + s = 4.141009439 Solving 6.07142857 + s = 4.141009439 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6.07142857' to each side of the equation. 6.07142857 + -6.07142857 + s = 4.141009439 + -6.07142857 Combine like terms: 6.07142857 + -6.07142857 = 0.00000000 0.00000000 + s = 4.141009439 + -6.07142857 s = 4.141009439 + -6.07142857 Combine like terms: 4.141009439 + -6.07142857 = -1.930419131 s = -1.930419131 Simplifying s = -1.930419131Subproblem 2
s + 6.07142857 = -4.141009439 Simplifying s + 6.07142857 = -4.141009439 Reorder the terms: 6.07142857 + s = -4.141009439 Solving 6.07142857 + s = -4.141009439 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6.07142857' to each side of the equation. 6.07142857 + -6.07142857 + s = -4.141009439 + -6.07142857 Combine like terms: 6.07142857 + -6.07142857 = 0.00000000 0.00000000 + s = -4.141009439 + -6.07142857 s = -4.141009439 + -6.07142857 Combine like terms: -4.141009439 + -6.07142857 = -10.212438009 s = -10.212438009 Simplifying s = -10.212438009Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.930419131, -10.212438009}
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