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Simplifying s2 + 4s + -80 = 0 Reorder the terms: -80 + 4s + s2 = 0 Solving -80 + 4s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 4s + 80 + s2 = 0 + 80 Reorder the terms: -80 + 80 + 4s + s2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 4s + s2 = 0 + 80 4s + s2 = 0 + 80 Combine like terms: 0 + 80 = 80 4s + s2 = 80 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = 80 + 4 Reorder the terms: 4 + 4s + s2 = 80 + 4 Combine like terms: 80 + 4 = 84 4 + 4s + s2 = 84 Factor a perfect square on the left side: (s + 2)(s + 2) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (s + 2) equal to 9.16515139 and -9.16515139.Subproblem 1
s + 2 = 9.16515139 Simplifying s + 2 = 9.16515139 Reorder the terms: 2 + s = 9.16515139 Solving 2 + s = 9.16515139 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + s = 9.16515139 + -2 s = 9.16515139 + -2 Combine like terms: 9.16515139 + -2 = 7.16515139 s = 7.16515139 Simplifying s = 7.16515139Subproblem 2
s + 2 = -9.16515139 Simplifying s + 2 = -9.16515139 Reorder the terms: 2 + s = -9.16515139 Solving 2 + s = -9.16515139 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + s = -9.16515139 + -2 s = -9.16515139 + -2 Combine like terms: -9.16515139 + -2 = -11.16515139 s = -11.16515139 Simplifying s = -11.16515139Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.16515139, -11.16515139}
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