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Simplifying 2s2 + 20s + 33 = 0 Reorder the terms: 33 + 20s + 2s2 = 0 Solving 33 + 20s + 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'. 16.5 + 10s + s2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + 10s + -16.5 + s2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + 10s + s2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + 10s + s2 = 0 + -16.5 10s + s2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 10s + s2 = -16.5 The s term is 10s. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10s + 25 + s2 = -16.5 + 25 Reorder the terms: 25 + 10s + s2 = -16.5 + 25 Combine like terms: -16.5 + 25 = 8.5 25 + 10s + s2 = 8.5 Factor a perfect square on the left side: (s + 5)(s + 5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (s + 5) equal to 2.915475947 and -2.915475947.Subproblem 1
s + 5 = 2.915475947 Simplifying s + 5 = 2.915475947 Reorder the terms: 5 + s = 2.915475947 Solving 5 + s = 2.915475947 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = 2.915475947 + -5 Combine like terms: 5 + -5 = 0 0 + s = 2.915475947 + -5 s = 2.915475947 + -5 Combine like terms: 2.915475947 + -5 = -2.084524053 s = -2.084524053 Simplifying s = -2.084524053Subproblem 2
s + 5 = -2.915475947 Simplifying s + 5 = -2.915475947 Reorder the terms: 5 + s = -2.915475947 Solving 5 + s = -2.915475947 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = -2.915475947 + -5 Combine like terms: 5 + -5 = 0 0 + s = -2.915475947 + -5 s = -2.915475947 + -5 Combine like terms: -2.915475947 + -5 = -7.915475947 s = -7.915475947 Simplifying s = -7.915475947Solution
The solution to the problem is based on the solutions from the subproblems. s = {-2.084524053, -7.915475947}
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