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Simplifying s + -4 + -1(s2 + -2) + -8s = 0 Reorder the terms: s + -4 + -1(-2 + s2) + -8s = 0 s + -4 + (-2 * -1 + s2 * -1) + -8s = 0 s + -4 + (2 + -1s2) + -8s = 0 Reorder the terms: -4 + 2 + s + -8s + -1s2 = 0 Combine like terms: -4 + 2 = -2 -2 + s + -8s + -1s2 = 0 Combine like terms: s + -8s = -7s -2 + -7s + -1s2 = 0 Solving -2 + -7s + -1s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 7s + s2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 7s + s2)' equal to zero and attempt to solve: Simplifying 2 + 7s + s2 = 0 Solving 2 + 7s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7s + -2 + s2 = 0 + -2 Reorder the terms: 2 + -2 + 7s + s2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7s + s2 = 0 + -2 7s + s2 = 0 + -2 Combine like terms: 0 + -2 = -2 7s + s2 = -2 The s term is 7s. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7s + 12.25 + s2 = -2 + 12.25 Reorder the terms: 12.25 + 7s + s2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + 7s + s2 = 10.25 Factor a perfect square on the left side: (s + 3.5)(s + 3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (s + 3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
s + 3.5 = 3.201562119 Simplifying s + 3.5 = 3.201562119 Reorder the terms: 3.5 + s = 3.201562119 Solving 3.5 + s = 3.201562119 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + s = 3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + s = 3.201562119 + -3.5 s = 3.201562119 + -3.5 Combine like terms: 3.201562119 + -3.5 = -0.298437881 s = -0.298437881 Simplifying s = -0.298437881Subproblem 2
s + 3.5 = -3.201562119 Simplifying s + 3.5 = -3.201562119 Reorder the terms: 3.5 + s = -3.201562119 Solving 3.5 + s = -3.201562119 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + s = -3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + s = -3.201562119 + -3.5 s = -3.201562119 + -3.5 Combine like terms: -3.201562119 + -3.5 = -6.701562119 s = -6.701562119 Simplifying s = -6.701562119Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.298437881, -6.701562119}Solution
s = {-0.298437881, -6.701562119}
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