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Simplifying (s2 + 3s + -4) + (5s + -2) = 0 Reorder the terms: (-4 + 3s + s2) + (5s + -2) = 0 Remove parenthesis around (-4 + 3s + s2) -4 + 3s + s2 + (5s + -2) = 0 Reorder the terms: -4 + 3s + s2 + (-2 + 5s) = 0 Remove parenthesis around (-2 + 5s) -4 + 3s + s2 + -2 + 5s = 0 Reorder the terms: -4 + -2 + 3s + 5s + s2 = 0 Combine like terms: -4 + -2 = -6 -6 + 3s + 5s + s2 = 0 Combine like terms: 3s + 5s = 8s -6 + 8s + s2 = 0 Solving -6 + 8s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 8s + 6 + s2 = 0 + 6 Reorder the terms: -6 + 6 + 8s + s2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 8s + s2 = 0 + 6 8s + s2 = 0 + 6 Combine like terms: 0 + 6 = 6 8s + s2 = 6 The s term is 8s. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8s + 16 + s2 = 6 + 16 Reorder the terms: 16 + 8s + s2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + 8s + s2 = 22 Factor a perfect square on the left side: (s + 4)(s + 4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (s + 4) equal to 4.69041576 and -4.69041576.Subproblem 1
s + 4 = 4.69041576 Simplifying s + 4 = 4.69041576 Reorder the terms: 4 + s = 4.69041576 Solving 4 + s = 4.69041576 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + s = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + s = 4.69041576 + -4 s = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 s = 0.69041576 Simplifying s = 0.69041576Subproblem 2
s + 4 = -4.69041576 Simplifying s + 4 = -4.69041576 Reorder the terms: 4 + s = -4.69041576 Solving 4 + s = -4.69041576 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + s = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + s = -4.69041576 + -4 s = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 s = -8.69041576 Simplifying s = -8.69041576Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.69041576, -8.69041576}
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