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Simplifying s2 + 12s = 32 Reorder the terms: 12s + s2 = 32 Solving 12s + s2 = 32 Solving for variable 's'. Reorder the terms: -32 + 12s + s2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 12s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 12s + 32 + s2 = 0 + 32 Reorder the terms: -32 + 32 + 12s + s2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 12s + s2 = 0 + 32 12s + s2 = 0 + 32 Combine like terms: 0 + 32 = 32 12s + s2 = 32 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 = 32 + 36 Reorder the terms: 36 + 12s + s2 = 32 + 36 Combine like terms: 32 + 36 = 68 36 + 12s + s2 = 68 Factor a perfect square on the left side: (s + 6)(s + 6) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (s + 6) equal to 8.246211251 and -8.246211251.Subproblem 1
s + 6 = 8.246211251 Simplifying s + 6 = 8.246211251 Reorder the terms: 6 + s = 8.246211251 Solving 6 + s = 8.246211251 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 = 8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + s = 8.246211251 + -6 s = 8.246211251 + -6 Combine like terms: 8.246211251 + -6 = 2.246211251 s = 2.246211251 Simplifying s = 2.246211251Subproblem 2
s + 6 = -8.246211251 Simplifying s + 6 = -8.246211251 Reorder the terms: 6 + s = -8.246211251 Solving 6 + s = -8.246211251 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 = -8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + s = -8.246211251 + -6 s = -8.246211251 + -6 Combine like terms: -8.246211251 + -6 = -14.246211251 s = -14.246211251 Simplifying s = -14.246211251Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.246211251, -14.246211251}
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