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Simplifying (s + 4)(s + -4) = -2s Reorder the terms: (4 + s)(s + -4) = -2s Reorder the terms: (4 + s)(-4 + s) = -2s Multiply (4 + s) * (-4 + s) (4(-4 + s) + s(-4 + s)) = -2s ((-4 * 4 + s * 4) + s(-4 + s)) = -2s ((-16 + 4s) + s(-4 + s)) = -2s (-16 + 4s + (-4 * s + s * s)) = -2s (-16 + 4s + (-4s + s2)) = -2s Combine like terms: 4s + -4s = 0 (-16 + 0 + s2) = -2s (-16 + s2) = -2s Solving -16 + s2 = -2s Solving for variable 's'. Reorder the terms: -16 + 2s + s2 = -2s + 2s Combine like terms: -2s + 2s = 0 -16 + 2s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 2s + 16 + s2 = 0 + 16 Reorder the terms: -16 + 16 + 2s + s2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2s + s2 = 0 + 16 2s + s2 = 0 + 16 Combine like terms: 0 + 16 = 16 2s + s2 = 16 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 16 + 1 Reorder the terms: 1 + 2s + s2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2s + s2 = 17 Factor a perfect square on the left side: (s + 1)(s + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (s + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
s + 1 = 4.123105626 Simplifying s + 1 = 4.123105626 Reorder the terms: 1 + s = 4.123105626 Solving 1 + s = 4.123105626 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + s = 4.123105626 + -1 s = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 s = 3.123105626 Simplifying s = 3.123105626Subproblem 2
s + 1 = -4.123105626 Simplifying s + 1 = -4.123105626 Reorder the terms: 1 + s = -4.123105626 Solving 1 + s = -4.123105626 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + s = -4.123105626 + -1 s = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 s = -5.123105626 Simplifying s = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.123105626, -5.123105626}
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