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Simplifying 2s2 + -13s + -16 = 0 Reorder the terms: -16 + -13s + 2s2 = 0 Solving -16 + -13s + 2s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -6.5s + s2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -6.5s + 8 + s2 = 0 + 8 Reorder the terms: -8 + 8 + -6.5s + s2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6.5s + s2 = 0 + 8 -6.5s + s2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6.5s + s2 = 8 The s term is -6.5s. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5s + 10.5625 + s2 = 8 + 10.5625 Reorder the terms: 10.5625 + -6.5s + s2 = 8 + 10.5625 Combine like terms: 8 + 10.5625 = 18.5625 10.5625 + -6.5s + s2 = 18.5625 Factor a perfect square on the left side: (s + -3.25)(s + -3.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (s + -3.25) equal to 4.308421985 and -4.308421985.Subproblem 1
s + -3.25 = 4.308421985 Simplifying s + -3.25 = 4.308421985 Reorder the terms: -3.25 + s = 4.308421985 Solving -3.25 + s = 4.308421985 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + s = 4.308421985 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + s = 4.308421985 + 3.25 s = 4.308421985 + 3.25 Combine like terms: 4.308421985 + 3.25 = 7.558421985 s = 7.558421985 Simplifying s = 7.558421985Subproblem 2
s + -3.25 = -4.308421985 Simplifying s + -3.25 = -4.308421985 Reorder the terms: -3.25 + s = -4.308421985 Solving -3.25 + s = -4.308421985 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + s = -4.308421985 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + s = -4.308421985 + 3.25 s = -4.308421985 + 3.25 Combine like terms: -4.308421985 + 3.25 = -1.058421985 s = -1.058421985 Simplifying s = -1.058421985Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.558421985, -1.058421985}
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