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Simplifying s2 + 12s + 21 = 0 Reorder the terms: 21 + 12s + s2 = 0 Solving 21 + 12s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 12s + -21 + s2 = 0 + -21 Reorder the terms: 21 + -21 + 12s + s2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 12s + s2 = 0 + -21 12s + s2 = 0 + -21 Combine like terms: 0 + -21 = -21 12s + s2 = -21 The s term is 12s. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12s + 36 + s2 = -21 + 36 Reorder the terms: 36 + 12s + s2 = -21 + 36 Combine like terms: -21 + 36 = 15 36 + 12s + s2 = 15 Factor a perfect square on the left side: (s + 6)(s + 6) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (s + 6) equal to 3.872983346 and -3.872983346.Subproblem 1
s + 6 = 3.872983346 Simplifying s + 6 = 3.872983346 Reorder the terms: 6 + s = 3.872983346 Solving 6 + s = 3.872983346 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = 3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + s = 3.872983346 + -6 s = 3.872983346 + -6 Combine like terms: 3.872983346 + -6 = -2.127016654 s = -2.127016654 Simplifying s = -2.127016654Subproblem 2
s + 6 = -3.872983346 Simplifying s + 6 = -3.872983346 Reorder the terms: 6 + s = -3.872983346 Solving 6 + s = -3.872983346 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = -3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + s = -3.872983346 + -6 s = -3.872983346 + -6 Combine like terms: -3.872983346 + -6 = -9.872983346 s = -9.872983346 Simplifying s = -9.872983346Solution
The solution to the problem is based on the solutions from the subproblems. s = {-2.127016654, -9.872983346}
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