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Simplifying 169 = s2 + 3s + 9 Reorder the terms: 169 = 9 + 3s + s2 Solving 169 = 9 + 3s + s2 Solving for variable 's'. Combine like terms: 169 + -9 = 160 160 + -3s + -1s2 = 9 + 3s + s2 + -9 + -3s + -1s2 Reorder the terms: 160 + -3s + -1s2 = 9 + -9 + 3s + -3s + s2 + -1s2 Combine like terms: 9 + -9 = 0 160 + -3s + -1s2 = 0 + 3s + -3s + s2 + -1s2 160 + -3s + -1s2 = 3s + -3s + s2 + -1s2 Combine like terms: 3s + -3s = 0 160 + -3s + -1s2 = 0 + s2 + -1s2 160 + -3s + -1s2 = s2 + -1s2 Combine like terms: s2 + -1s2 = 0 160 + -3s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -160 + 3s + s2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 3s + 160 + s2 = 0 + 160 Reorder the terms: -160 + 160 + 3s + s2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 3s + s2 = 0 + 160 3s + s2 = 0 + 160 Combine like terms: 0 + 160 = 160 3s + s2 = 160 The s term is 3s. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3s + 2.25 + s2 = 160 + 2.25 Reorder the terms: 2.25 + 3s + s2 = 160 + 2.25 Combine like terms: 160 + 2.25 = 162.25 2.25 + 3s + s2 = 162.25 Factor a perfect square on the left side: (s + 1.5)(s + 1.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (s + 1.5) equal to 12.737739203 and -12.737739203.Subproblem 1
s + 1.5 = 12.737739203 Simplifying s + 1.5 = 12.737739203 Reorder the terms: 1.5 + s = 12.737739203 Solving 1.5 + s = 12.737739203 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + s = 12.737739203 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = 12.737739203 + -1.5 s = 12.737739203 + -1.5 Combine like terms: 12.737739203 + -1.5 = 11.237739203 s = 11.237739203 Simplifying s = 11.237739203Subproblem 2
s + 1.5 = -12.737739203 Simplifying s + 1.5 = -12.737739203 Reorder the terms: 1.5 + s = -12.737739203 Solving 1.5 + s = -12.737739203 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + s = -12.737739203 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = -12.737739203 + -1.5 s = -12.737739203 + -1.5 Combine like terms: -12.737739203 + -1.5 = -14.237739203 s = -14.237739203 Simplifying s = -14.237739203Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.237739203, -14.237739203}
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