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Simplifying s2 + 7s + -196 = 0 Reorder the terms: -196 + 7s + s2 = 0 Solving -196 + 7s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 7s + 196 + s2 = 0 + 196 Reorder the terms: -196 + 196 + 7s + s2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 7s + s2 = 0 + 196 7s + s2 = 0 + 196 Combine like terms: 0 + 196 = 196 7s + s2 = 196 The s term is 7s. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7s + 12.25 + s2 = 196 + 12.25 Reorder the terms: 12.25 + 7s + s2 = 196 + 12.25 Combine like terms: 196 + 12.25 = 208.25 12.25 + 7s + s2 = 208.25 Factor a perfect square on the left side: (s + 3.5)(s + 3.5) = 208.25 Calculate the square root of the right side: 14.43086969 Break this problem into two subproblems by setting (s + 3.5) equal to 14.43086969 and -14.43086969.Subproblem 1
s + 3.5 = 14.43086969 Simplifying s + 3.5 = 14.43086969 Reorder the terms: 3.5 + s = 14.43086969 Solving 3.5 + s = 14.43086969 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + s = 14.43086969 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + s = 14.43086969 + -3.5 s = 14.43086969 + -3.5 Combine like terms: 14.43086969 + -3.5 = 10.93086969 s = 10.93086969 Simplifying s = 10.93086969Subproblem 2
s + 3.5 = -14.43086969 Simplifying s + 3.5 = -14.43086969 Reorder the terms: 3.5 + s = -14.43086969 Solving 3.5 + s = -14.43086969 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + s = -14.43086969 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + s = -14.43086969 + -3.5 s = -14.43086969 + -3.5 Combine like terms: -14.43086969 + -3.5 = -17.93086969 s = -17.93086969 Simplifying s = -17.93086969Solution
The solution to the problem is based on the solutions from the subproblems. s = {10.93086969, -17.93086969}
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