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Simplifying 2s2 + 9s + 2 = 0 Reorder the terms: 2 + 9s + 2s2 = 0 Solving 2 + 9s + 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'. 1 + 4.5s + s2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.5s + -1 + s2 = 0 + -1 Reorder the terms: 1 + -1 + 4.5s + s2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.5s + s2 = 0 + -1 4.5s + s2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.5s + s2 = -1 The s term is 4.5s. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5s + 5.0625 + s2 = -1 + 5.0625 Reorder the terms: 5.0625 + 4.5s + s2 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + 4.5s + s2 = 4.0625 Factor a perfect square on the left side: (s + 2.25)(s + 2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (s + 2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
s + 2.25 = 2.015564437 Simplifying s + 2.25 = 2.015564437 Reorder the terms: 2.25 + s = 2.015564437 Solving 2.25 + s = 2.015564437 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + s = 2.015564437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + s = 2.015564437 + -2.25 s = 2.015564437 + -2.25 Combine like terms: 2.015564437 + -2.25 = -0.234435563 s = -0.234435563 Simplifying s = -0.234435563Subproblem 2
s + 2.25 = -2.015564437 Simplifying s + 2.25 = -2.015564437 Reorder the terms: 2.25 + s = -2.015564437 Solving 2.25 + s = -2.015564437 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + s = -2.015564437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + s = -2.015564437 + -2.25 s = -2.015564437 + -2.25 Combine like terms: -2.015564437 + -2.25 = -4.265564437 s = -4.265564437 Simplifying s = -4.265564437Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.234435563, -4.265564437}
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