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Simplifying -8s2 + 9s + 6 = 0 Reorder the terms: 6 + 9s + -8s2 = 0 Solving 6 + 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'. -0.75 + -1.125s + s2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.125s + 0.75 + s2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.125s + s2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.125s + s2 = 0 + 0.75 -1.125s + s2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.125s + s2 = 0.75 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 = 0.75 + 0.31640625 Reorder the terms: 0.31640625 + -1.125s + s2 = 0.75 + 0.31640625 Combine like terms: 0.75 + 0.31640625 = 1.06640625 0.31640625 + -1.125s + s2 = 1.06640625 Factor a perfect square on the left side: (s + -0.5625)(s + -0.5625) = 1.06640625 Calculate the square root of the right side: 1.032669478 Break this problem into two subproblems by setting (s + -0.5625) equal to 1.032669478 and -1.032669478.Subproblem 1
s + -0.5625 = 1.032669478 Simplifying s + -0.5625 = 1.032669478 Reorder the terms: -0.5625 + s = 1.032669478 Solving -0.5625 + s = 1.032669478 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 = 1.032669478 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + s = 1.032669478 + 0.5625 s = 1.032669478 + 0.5625 Combine like terms: 1.032669478 + 0.5625 = 1.595169478 s = 1.595169478 Simplifying s = 1.595169478Subproblem 2
s + -0.5625 = -1.032669478 Simplifying s + -0.5625 = -1.032669478 Reorder the terms: -0.5625 + s = -1.032669478 Solving -0.5625 + s = -1.032669478 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 = -1.032669478 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + s = -1.032669478 + 0.5625 s = -1.032669478 + 0.5625 Combine like terms: -1.032669478 + 0.5625 = -0.470169478 s = -0.470169478 Simplifying s = -0.470169478Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.595169478, -0.470169478}
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