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Simplifying 4s2 + 16s + -8 = 0 Reorder the terms: -8 + 16s + 4s2 = 0 Solving -8 + 16s + 4s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 4s + s2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 4s + s2)' equal to zero and attempt to solve: Simplifying -2 + 4s + s2 = 0 Solving -2 + 4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4s + 2 + s2 = 0 + 2 Reorder the terms: -2 + 2 + 4s + s2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4s + s2 = 0 + 2 4s + s2 = 0 + 2 Combine like terms: 0 + 2 = 2 4s + s2 = 2 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 = 2 + 4 Reorder the terms: 4 + 4s + s2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4s + s2 = 6 Factor a perfect square on the left side: (s + 2)(s + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (s + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
s + 2 = 2.449489743 Simplifying s + 2 = 2.449489743 Reorder the terms: 2 + s = 2.449489743 Solving 2 + s = 2.449489743 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 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + s = 2.449489743 + -2 s = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 s = 0.449489743 Simplifying s = 0.449489743Subproblem 2
s + 2 = -2.449489743 Simplifying s + 2 = -2.449489743 Reorder the terms: 2 + s = -2.449489743 Solving 2 + s = -2.449489743 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 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + s = -2.449489743 + -2 s = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 s = -4.449489743 Simplifying s = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.449489743, -4.449489743}Solution
s = {0.449489743, -4.449489743}
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