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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'. 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 = 0.820194102 s = 0.820194102 Simplifying s = 0.820194102Subproblem 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 = 0.304805898 s = 0.304805898 Simplifying s = 0.304805898Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.820194102, 0.304805898}
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