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Simplifying s2 + 14s + -31 = 33 Reorder the terms: -31 + 14s + s2 = 33 Solving -31 + 14s + s2 = 33 Solving for variable 's'. Reorder the terms: -31 + -33 + 14s + s2 = 33 + -33 Combine like terms: -31 + -33 = -64 -64 + 14s + s2 = 33 + -33 Combine like terms: 33 + -33 = 0 -64 + 14s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 14s + 64 + s2 = 0 + 64 Reorder the terms: -64 + 64 + 14s + s2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 14s + s2 = 0 + 64 14s + s2 = 0 + 64 Combine like terms: 0 + 64 = 64 14s + s2 = 64 The s term is 14s. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14s + 49 + s2 = 64 + 49 Reorder the terms: 49 + 14s + s2 = 64 + 49 Combine like terms: 64 + 49 = 113 49 + 14s + s2 = 113 Factor a perfect square on the left side: (s + 7)(s + 7) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (s + 7) equal to 10.630145813 and -10.630145813.Subproblem 1
s + 7 = 10.630145813 Simplifying s + 7 = 10.630145813 Reorder the terms: 7 + s = 10.630145813 Solving 7 + s = 10.630145813 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + s = 10.630145813 + -7 Combine like terms: 7 + -7 = 0 0 + s = 10.630145813 + -7 s = 10.630145813 + -7 Combine like terms: 10.630145813 + -7 = 3.630145813 s = 3.630145813 Simplifying s = 3.630145813Subproblem 2
s + 7 = -10.630145813 Simplifying s + 7 = -10.630145813 Reorder the terms: 7 + s = -10.630145813 Solving 7 + s = -10.630145813 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + s = -10.630145813 + -7 Combine like terms: 7 + -7 = 0 0 + s = -10.630145813 + -7 s = -10.630145813 + -7 Combine like terms: -10.630145813 + -7 = -17.630145813 s = -17.630145813 Simplifying s = -17.630145813Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.630145813, -17.630145813}
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