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Simplifying 38s + -16s2 + 1250 = 0 Reorder the terms: 1250 + 38s + -16s2 = 0 Solving 1250 + 38s + -16s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(625 + 19s + -8s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(625 + 19s + -8s2)' equal to zero and attempt to solve: Simplifying 625 + 19s + -8s2 = 0 Solving 625 + 19s + -8s2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -78.125 + -2.375s + s2 = 0 Move the constant term to the right: Add '78.125' to each side of the equation. -78.125 + -2.375s + 78.125 + s2 = 0 + 78.125 Reorder the terms: -78.125 + 78.125 + -2.375s + s2 = 0 + 78.125 Combine like terms: -78.125 + 78.125 = 0.000 0.000 + -2.375s + s2 = 0 + 78.125 -2.375s + s2 = 0 + 78.125 Combine like terms: 0 + 78.125 = 78.125 -2.375s + s2 = 78.125 The s term is -2.375s. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375s + 1.41015625 + s2 = 78.125 + 1.41015625 Reorder the terms: 1.41015625 + -2.375s + s2 = 78.125 + 1.41015625 Combine like terms: 78.125 + 1.41015625 = 79.53515625 1.41015625 + -2.375s + s2 = 79.53515625 Factor a perfect square on the left side: (s + -1.1875)(s + -1.1875) = 79.53515625 Calculate the square root of the right side: 8.918248497 Break this problem into two subproblems by setting (s + -1.1875) equal to 8.918248497 and -8.918248497.Subproblem 1
s + -1.1875 = 8.918248497 Simplifying s + -1.1875 = 8.918248497 Reorder the terms: -1.1875 + s = 8.918248497 Solving -1.1875 + s = 8.918248497 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + s = 8.918248497 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + s = 8.918248497 + 1.1875 s = 8.918248497 + 1.1875 Combine like terms: 8.918248497 + 1.1875 = 10.105748497 s = 10.105748497 Simplifying s = 10.105748497Subproblem 2
s + -1.1875 = -8.918248497 Simplifying s + -1.1875 = -8.918248497 Reorder the terms: -1.1875 + s = -8.918248497 Solving -1.1875 + s = -8.918248497 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + s = -8.918248497 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + s = -8.918248497 + 1.1875 s = -8.918248497 + 1.1875 Combine like terms: -8.918248497 + 1.1875 = -7.730748497 s = -7.730748497 Simplifying s = -7.730748497Solution
The solution to the problem is based on the solutions from the subproblems. s = {10.105748497, -7.730748497}Solution
s = {10.105748497, -7.730748497}
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