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Simplifying s2 + 6s + -3 = 0 Reorder the terms: -3 + 6s + s2 = 0 Solving -3 + 6s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6s + 3 + s2 = 0 + 3 Reorder the terms: -3 + 3 + 6s + s2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6s + s2 = 0 + 3 6s + s2 = 0 + 3 Combine like terms: 0 + 3 = 3 6s + s2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6s + s2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6s + s2 = 12 Factor a perfect square on the left side: (s + 3)(s + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (s + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
s + 3 = 3.464101615 Simplifying s + 3 = 3.464101615 Reorder the terms: 3 + s = 3.464101615 Solving 3 + s = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + s = 3.464101615 + -3 s = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 s = 0.464101615 Simplifying s = 0.464101615Subproblem 2
s + 3 = -3.464101615 Simplifying s + 3 = -3.464101615 Reorder the terms: 3 + s = -3.464101615 Solving 3 + s = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + s = -3.464101615 + -3 s = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 s = -6.464101615 Simplifying s = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.464101615, -6.464101615}
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