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Simplifying 9s2 + -324s + 648 = 0 Reorder the terms: 648 + -324s + 9s2 = 0 Solving 648 + -324s + 9s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '9'. 9(72 + -36s + s2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(72 + -36s + s2)' equal to zero and attempt to solve: Simplifying 72 + -36s + s2 = 0 Solving 72 + -36s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -36s + -72 + s2 = 0 + -72 Reorder the terms: 72 + -72 + -36s + s2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -36s + s2 = 0 + -72 -36s + s2 = 0 + -72 Combine like terms: 0 + -72 = -72 -36s + s2 = -72 The s term is -36s. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36s + 324 + s2 = -72 + 324 Reorder the terms: 324 + -36s + s2 = -72 + 324 Combine like terms: -72 + 324 = 252 324 + -36s + s2 = 252 Factor a perfect square on the left side: (s + -18)(s + -18) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (s + -18) equal to 15.874507866 and -15.874507866.Subproblem 1
s + -18 = 15.874507866 Simplifying s + -18 = 15.874507866 Reorder the terms: -18 + s = 15.874507866 Solving -18 + s = 15.874507866 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + s = 15.874507866 + 18 Combine like terms: -18 + 18 = 0 0 + s = 15.874507866 + 18 s = 15.874507866 + 18 Combine like terms: 15.874507866 + 18 = 33.874507866 s = 33.874507866 Simplifying s = 33.874507866Subproblem 2
s + -18 = -15.874507866 Simplifying s + -18 = -15.874507866 Reorder the terms: -18 + s = -15.874507866 Solving -18 + s = -15.874507866 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + s = -15.874507866 + 18 Combine like terms: -18 + 18 = 0 0 + s = -15.874507866 + 18 s = -15.874507866 + 18 Combine like terms: -15.874507866 + 18 = 2.125492134 s = 2.125492134 Simplifying s = 2.125492134Solution
The solution to the problem is based on the solutions from the subproblems. s = {33.874507866, 2.125492134}Solution
s = {33.874507866, 2.125492134}
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