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Simplifying 2s4 + 12s2 + -16 = 0 Reorder the terms: -16 + 12s2 + 2s4 = 0 Solving -16 + 12s2 + 2s4 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 6s2 + s4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 6s2 + s4)' equal to zero and attempt to solve: Simplifying -8 + 6s2 + s4 = 0 Solving -8 + 6s2 + s4 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6s2 + 8 + s4 = 0 + 8 Reorder the terms: -8 + 8 + 6s2 + s4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6s2 + s4 = 0 + 8 6s2 + s4 = 0 + 8 Combine like terms: 0 + 8 = 8 6s2 + s4 = 8 The s term is 6s2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6s2 + 9 + s4 = 8 + 9 Reorder the terms: 9 + 6s2 + s4 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6s2 + s4 = 17 Factor a perfect square on the left side: (s2 + 3)(s2 + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (s2 + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
s2 + 3 = 4.123105626 Simplifying s2 + 3 = 4.123105626 Reorder the terms: 3 + s2 = 4.123105626 Solving 3 + s2 = 4.123105626 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s2 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + s2 = 4.123105626 + -3 s2 = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 s2 = 1.123105626 Simplifying s2 = 1.123105626 Take the square root of each side: s = {-1.059766779, 1.059766779}Subproblem 2
s2 + 3 = -4.123105626 Simplifying s2 + 3 = -4.123105626 Reorder the terms: 3 + s2 = -4.123105626 Solving 3 + s2 = -4.123105626 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s2 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + s2 = -4.123105626 + -3 s2 = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 s2 = -7.123105626 Simplifying s2 = -7.123105626 Reorder the terms: 7.123105626 + s2 = -7.123105626 + 7.123105626 Combine like terms: -7.123105626 + 7.123105626 = 0.000000000 7.123105626 + s2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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