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Simplifying -8s2 + -9s + -2 = 0 Reorder the terms: -2 + -9s + -8s2 = 0 Solving -2 + -9s + -8s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 9s + 8s2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 9s + 8s2)' equal to zero and attempt to solve: Simplifying 2 + 9s + 8s2 = 0 Solving 2 + 9s + 8s2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + 1.125s + s2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.125s + -0.25 + s2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.125s + s2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.125s + s2 = 0 + -0.25 1.125s + s2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.125s + s2 = -0.25 The s term is 1.125s. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125s + 0.31640625 + s2 = -0.25 + 0.31640625 Reorder the terms: 0.31640625 + 1.125s + s2 = -0.25 + 0.31640625 Combine like terms: -0.25 + 0.31640625 = 0.06640625 0.31640625 + 1.125s + s2 = 0.06640625 Factor a perfect square on the left side: (s + 0.5625)(s + 0.5625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (s + 0.5625) equal to 0.257694102 and -0.257694102.Subproblem 1
s + 0.5625 = 0.257694102 Simplifying s + 0.5625 = 0.257694102 Reorder the terms: 0.5625 + s = 0.257694102 Solving 0.5625 + s = 0.257694102 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + s = 0.257694102 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + s = 0.257694102 + -0.5625 s = 0.257694102 + -0.5625 Combine like terms: 0.257694102 + -0.5625 = -0.304805898 s = -0.304805898 Simplifying s = -0.304805898Subproblem 2
s + 0.5625 = -0.257694102 Simplifying s + 0.5625 = -0.257694102 Reorder the terms: 0.5625 + s = -0.257694102 Solving 0.5625 + s = -0.257694102 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + s = -0.257694102 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + s = -0.257694102 + -0.5625 s = -0.257694102 + -0.5625 Combine like terms: -0.257694102 + -0.5625 = -0.820194102 s = -0.820194102 Simplifying s = -0.820194102Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.304805898, -0.820194102}Solution
s = {-0.304805898, -0.820194102}
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