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Simplifying s2 + 16s + 4 = 0 Reorder the terms: 4 + 16s + s2 = 0 Solving 4 + 16s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 16s + -4 + s2 = 0 + -4 Reorder the terms: 4 + -4 + 16s + s2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 16s + s2 = 0 + -4 16s + s2 = 0 + -4 Combine like terms: 0 + -4 = -4 16s + s2 = -4 The s term is 16s. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16s + 64 + s2 = -4 + 64 Reorder the terms: 64 + 16s + s2 = -4 + 64 Combine like terms: -4 + 64 = 60 64 + 16s + s2 = 60 Factor a perfect square on the left side: (s + 8)(s + 8) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (s + 8) equal to 7.745966692 and -7.745966692.Subproblem 1
s + 8 = 7.745966692 Simplifying s + 8 = 7.745966692 Reorder the terms: 8 + s = 7.745966692 Solving 8 + s = 7.745966692 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = 7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + s = 7.745966692 + -8 s = 7.745966692 + -8 Combine like terms: 7.745966692 + -8 = -0.254033308 s = -0.254033308 Simplifying s = -0.254033308Subproblem 2
s + 8 = -7.745966692 Simplifying s + 8 = -7.745966692 Reorder the terms: 8 + s = -7.745966692 Solving 8 + s = -7.745966692 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = -7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + s = -7.745966692 + -8 s = -7.745966692 + -8 Combine like terms: -7.745966692 + -8 = -15.745966692 s = -15.745966692 Simplifying s = -15.745966692Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.254033308, -15.745966692}
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