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Simplifying s2 = 3 + s(1 + -5s) s2 = 3 + (1 * s + -5s * s) s2 = 3 + (1s + -5s2) Solving s2 = 3 + 1s + -5s2 Solving for variable 's'. Reorder the terms: -3 + -1s + s2 + 5s2 = 3 + 1s + -5s2 + -3 + -1s + 5s2 Combine like terms: s2 + 5s2 = 6s2 -3 + -1s + 6s2 = 3 + 1s + -5s2 + -3 + -1s + 5s2 Reorder the terms: -3 + -1s + 6s2 = 3 + -3 + 1s + -1s + -5s2 + 5s2 Combine like terms: 3 + -3 = 0 -3 + -1s + 6s2 = 0 + 1s + -1s + -5s2 + 5s2 -3 + -1s + 6s2 = 1s + -1s + -5s2 + 5s2 Combine like terms: 1s + -1s = 0 -3 + -1s + 6s2 = 0 + -5s2 + 5s2 -3 + -1s + 6s2 = -5s2 + 5s2 Combine like terms: -5s2 + 5s2 = 0 -3 + -1s + 6s2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -0.1666666667s + s2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.1666666667s + 0.5 + s2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.1666666667s + s2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.1666666667s + s2 = 0 + 0.5 -0.1666666667s + s2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.1666666667s + s2 = 0.5 The s term is -0.1666666667s. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667s + 0.006944444447 + s2 = 0.5 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667s + s2 = 0.5 + 0.006944444447 Combine like terms: 0.5 + 0.006944444447 = 0.506944444447 0.006944444447 + -0.1666666667s + s2 = 0.506944444447 Factor a perfect square on the left side: (s + -0.08333333335)(s + -0.08333333335) = 0.506944444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (s + -0.08333333335) equal to 0.712000312 and -0.712000312.Subproblem 1
s + -0.08333333335 = 0.712000312 Simplifying s + -0.08333333335 = 0.712000312 Reorder the terms: -0.08333333335 + s = 0.712000312 Solving -0.08333333335 + s = 0.712000312 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + s = 0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + s = 0.712000312 + 0.08333333335 s = 0.712000312 + 0.08333333335 Combine like terms: 0.712000312 + 0.08333333335 = 0.79533364535 s = 0.79533364535 Simplifying s = 0.79533364535Subproblem 2
s + -0.08333333335 = -0.712000312 Simplifying s + -0.08333333335 = -0.712000312 Reorder the terms: -0.08333333335 + s = -0.712000312 Solving -0.08333333335 + s = -0.712000312 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + s = -0.712000312 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + s = -0.712000312 + 0.08333333335 s = -0.712000312 + 0.08333333335 Combine like terms: -0.712000312 + 0.08333333335 = -0.62866697865 s = -0.62866697865 Simplifying s = -0.62866697865Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.79533364535, -0.62866697865}
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