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Simplifying 80s2 + 50s + -60 = 0 Reorder the terms: -60 + 50s + 80s2 = 0 Solving -60 + 50s + 80s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '10'. 10(-6 + 5s + 8s2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-6 + 5s + 8s2)' equal to zero and attempt to solve: Simplifying -6 + 5s + 8s2 = 0 Solving -6 + 5s + 8s2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + 0.625s + s2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.625s + 0.75 + s2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.625s + s2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.625s + s2 = 0 + 0.75 0.625s + s2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.625s + s2 = 0.75 The s term is 0.625s. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625s + 0.09765625 + s2 = 0.75 + 0.09765625 Reorder the terms: 0.09765625 + 0.625s + s2 = 0.75 + 0.09765625 Combine like terms: 0.75 + 0.09765625 = 0.84765625 0.09765625 + 0.625s + s2 = 0.84765625 Factor a perfect square on the left side: (s + 0.3125)(s + 0.3125) = 0.84765625 Calculate the square root of the right side: 0.920682491 Break this problem into two subproblems by setting (s + 0.3125) equal to 0.920682491 and -0.920682491.Subproblem 1
s + 0.3125 = 0.920682491 Simplifying s + 0.3125 = 0.920682491 Reorder the terms: 0.3125 + s = 0.920682491 Solving 0.3125 + s = 0.920682491 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + s = 0.920682491 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + s = 0.920682491 + -0.3125 s = 0.920682491 + -0.3125 Combine like terms: 0.920682491 + -0.3125 = 0.608182491 s = 0.608182491 Simplifying s = 0.608182491Subproblem 2
s + 0.3125 = -0.920682491 Simplifying s + 0.3125 = -0.920682491 Reorder the terms: 0.3125 + s = -0.920682491 Solving 0.3125 + s = -0.920682491 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + s = -0.920682491 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + s = -0.920682491 + -0.3125 s = -0.920682491 + -0.3125 Combine like terms: -0.920682491 + -0.3125 = -1.233182491 s = -1.233182491 Simplifying s = -1.233182491Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.608182491, -1.233182491}Solution
s = {0.608182491, -1.233182491}
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