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Simplifying s2 + 6s + -9 = 0 Reorder the terms: -9 + 6s + s2 = 0 Solving -9 + 6s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6s + 9 + s2 = 0 + 9 Reorder the terms: -9 + 9 + 6s + s2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6s + s2 = 0 + 9 6s + s2 = 0 + 9 Combine like terms: 0 + 9 = 9 6s + s2 = 9 The s term is 6s. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6s + 9 + s2 = 9 + 9 Reorder the terms: 9 + 6s + s2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6s + s2 = 18 Factor a perfect square on the left side: (s + 3)(s + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (s + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
s + 3 = 4.242640687 Simplifying s + 3 = 4.242640687 Reorder the terms: 3 + s = 4.242640687 Solving 3 + s = 4.242640687 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + s = 4.242640687 + -3 s = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 s = 1.242640687 Simplifying s = 1.242640687Subproblem 2
s + 3 = -4.242640687 Simplifying s + 3 = -4.242640687 Reorder the terms: 3 + s = -4.242640687 Solving 3 + s = -4.242640687 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + s = -4.242640687 + -3 s = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 s = -7.242640687 Simplifying s = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.242640687, -7.242640687}
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