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Simplifying 4s2 + 36s + 9 = 0 Reorder the terms: 9 + 36s + 4s2 = 0 Solving 9 + 36s + 4s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 9s + s2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 9s + -2.25 + s2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 9s + s2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 9s + s2 = 0 + -2.25 9s + s2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 9s + s2 = -2.25 The s term is 9s. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9s + 20.25 + s2 = -2.25 + 20.25 Reorder the terms: 20.25 + 9s + s2 = -2.25 + 20.25 Combine like terms: -2.25 + 20.25 = 18 20.25 + 9s + s2 = 18 Factor a perfect square on the left side: (s + 4.5)(s + 4.5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (s + 4.5) equal to 4.242640687 and -4.242640687.Subproblem 1
s + 4.5 = 4.242640687 Simplifying s + 4.5 = 4.242640687 Reorder the terms: 4.5 + s = 4.242640687 Solving 4.5 + s = 4.242640687 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + s = 4.242640687 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + s = 4.242640687 + -4.5 s = 4.242640687 + -4.5 Combine like terms: 4.242640687 + -4.5 = -0.257359313 s = -0.257359313 Simplifying s = -0.257359313Subproblem 2
s + 4.5 = -4.242640687 Simplifying s + 4.5 = -4.242640687 Reorder the terms: 4.5 + s = -4.242640687 Solving 4.5 + s = -4.242640687 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + s = -4.242640687 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + s = -4.242640687 + -4.5 s = -4.242640687 + -4.5 Combine like terms: -4.242640687 + -4.5 = -8.742640687 s = -8.742640687 Simplifying s = -8.742640687Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.257359313, -8.742640687}
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