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Simplifying 0 = -16s2 + 6s + 200 Reorder the terms: 0 = 200 + 6s + -16s2 Solving 0 = 200 + 6s + -16s2 Solving for variable 's'. Combine like terms: 0 + -200 = -200 -200 + -6s + 16s2 = 200 + 6s + -16s2 + -200 + -6s + 16s2 Reorder the terms: -200 + -6s + 16s2 = 200 + -200 + 6s + -6s + -16s2 + 16s2 Combine like terms: 200 + -200 = 0 -200 + -6s + 16s2 = 0 + 6s + -6s + -16s2 + 16s2 -200 + -6s + 16s2 = 6s + -6s + -16s2 + 16s2 Combine like terms: 6s + -6s = 0 -200 + -6s + 16s2 = 0 + -16s2 + 16s2 -200 + -6s + 16s2 = -16s2 + 16s2 Combine like terms: -16s2 + 16s2 = 0 -200 + -6s + 16s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + -3s + 8s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + -3s + 8s2)' equal to zero and attempt to solve: Simplifying -100 + -3s + 8s2 = 0 Solving -100 + -3s + 8s2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -12.5 + -0.375s + s2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.375s + 12.5 + s2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.375s + s2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.375s + s2 = 0 + 12.5 -0.375s + s2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.375s + s2 = 12.5 The s term is -0.375s. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375s + 0.03515625 + s2 = 12.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375s + s2 = 12.5 + 0.03515625 Combine like terms: 12.5 + 0.03515625 = 12.53515625 0.03515625 + -0.375s + s2 = 12.53515625 Factor a perfect square on the left side: (s + -0.1875)(s + -0.1875) = 12.53515625 Calculate the square root of the right side: 3.54050226 Break this problem into two subproblems by setting (s + -0.1875) equal to 3.54050226 and -3.54050226.Subproblem 1
s + -0.1875 = 3.54050226 Simplifying s + -0.1875 = 3.54050226 Reorder the terms: -0.1875 + s = 3.54050226 Solving -0.1875 + s = 3.54050226 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + s = 3.54050226 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + s = 3.54050226 + 0.1875 s = 3.54050226 + 0.1875 Combine like terms: 3.54050226 + 0.1875 = 3.72800226 s = 3.72800226 Simplifying s = 3.72800226Subproblem 2
s + -0.1875 = -3.54050226 Simplifying s + -0.1875 = -3.54050226 Reorder the terms: -0.1875 + s = -3.54050226 Solving -0.1875 + s = -3.54050226 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + s = -3.54050226 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + s = -3.54050226 + 0.1875 s = -3.54050226 + 0.1875 Combine like terms: -3.54050226 + 0.1875 = -3.35300226 s = -3.35300226 Simplifying s = -3.35300226Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.72800226, -3.35300226}Solution
s = {3.72800226, -3.35300226}
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