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Simplifying s2 + 12s + -51 = 0 Reorder the terms: -51 + 12s + s2 = 0 Solving -51 + 12s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 12s + 51 + s2 = 0 + 51 Reorder the terms: -51 + 51 + 12s + s2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 12s + s2 = 0 + 51 12s + s2 = 0 + 51 Combine like terms: 0 + 51 = 51 12s + s2 = 51 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 = 51 + 36 Reorder the terms: 36 + 12s + s2 = 51 + 36 Combine like terms: 51 + 36 = 87 36 + 12s + s2 = 87 Factor a perfect square on the left side: (s + 6)(s + 6) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (s + 6) equal to 9.327379053 and -9.327379053.Subproblem 1
s + 6 = 9.327379053 Simplifying s + 6 = 9.327379053 Reorder the terms: 6 + s = 9.327379053 Solving 6 + s = 9.327379053 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 = 9.327379053 + -6 Combine like terms: 6 + -6 = 0 0 + s = 9.327379053 + -6 s = 9.327379053 + -6 Combine like terms: 9.327379053 + -6 = 3.327379053 s = 3.327379053 Simplifying s = 3.327379053Subproblem 2
s + 6 = -9.327379053 Simplifying s + 6 = -9.327379053 Reorder the terms: 6 + s = -9.327379053 Solving 6 + s = -9.327379053 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 = -9.327379053 + -6 Combine like terms: 6 + -6 = 0 0 + s = -9.327379053 + -6 s = -9.327379053 + -6 Combine like terms: -9.327379053 + -6 = -15.327379053 s = -15.327379053 Simplifying s = -15.327379053Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.327379053, -15.327379053}
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