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Simplifying -3s2 + 57s = -39 Reorder the terms: 57s + -3s2 = -39 Solving 57s + -3s2 = -39 Solving for variable 's'. Reorder the terms: 39 + 57s + -3s2 = -39 + 39 Combine like terms: -39 + 39 = 0 39 + 57s + -3s2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(13 + 19s + -1s2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(13 + 19s + -1s2)' equal to zero and attempt to solve: Simplifying 13 + 19s + -1s2 = 0 Solving 13 + 19s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -19s + s2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -19s + 13 + s2 = 0 + 13 Reorder the terms: -13 + 13 + -19s + s2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -19s + s2 = 0 + 13 -19s + s2 = 0 + 13 Combine like terms: 0 + 13 = 13 -19s + s2 = 13 The s term is -19s. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19s + 90.25 + s2 = 13 + 90.25 Reorder the terms: 90.25 + -19s + s2 = 13 + 90.25 Combine like terms: 13 + 90.25 = 103.25 90.25 + -19s + s2 = 103.25 Factor a perfect square on the left side: (s + -9.5)(s + -9.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (s + -9.5) equal to 10.161200716 and -10.161200716.Subproblem 1
s + -9.5 = 10.161200716 Simplifying s + -9.5 = 10.161200716 Reorder the terms: -9.5 + s = 10.161200716 Solving -9.5 + s = 10.161200716 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + s = 10.161200716 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + s = 10.161200716 + 9.5 s = 10.161200716 + 9.5 Combine like terms: 10.161200716 + 9.5 = 19.661200716 s = 19.661200716 Simplifying s = 19.661200716Subproblem 2
s + -9.5 = -10.161200716 Simplifying s + -9.5 = -10.161200716 Reorder the terms: -9.5 + s = -10.161200716 Solving -9.5 + s = -10.161200716 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + s = -10.161200716 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + s = -10.161200716 + 9.5 s = -10.161200716 + 9.5 Combine like terms: -10.161200716 + 9.5 = -0.661200716 s = -0.661200716 Simplifying s = -0.661200716Solution
The solution to the problem is based on the solutions from the subproblems. s = {19.661200716, -0.661200716}Solution
s = {19.661200716, -0.661200716}
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