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Simplifying -2s2 + 52s + -74 = 0 Reorder the terms: -74 + 52s + -2s2 = 0 Solving -74 + 52s + -2s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(-37 + 26s + -1s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-37 + 26s + -1s2)' equal to zero and attempt to solve: Simplifying -37 + 26s + -1s2 = 0 Solving -37 + 26s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 37 + -26s + s2 = 0 Move the constant term to the right: Add '-37' to each side of the equation. 37 + -26s + -37 + s2 = 0 + -37 Reorder the terms: 37 + -37 + -26s + s2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -26s + s2 = 0 + -37 -26s + s2 = 0 + -37 Combine like terms: 0 + -37 = -37 -26s + s2 = -37 The s term is -26s. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26s + 169 + s2 = -37 + 169 Reorder the terms: 169 + -26s + s2 = -37 + 169 Combine like terms: -37 + 169 = 132 169 + -26s + s2 = 132 Factor a perfect square on the left side: (s + -13)(s + -13) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (s + -13) equal to 11.489125293 and -11.489125293.Subproblem 1
s + -13 = 11.489125293 Simplifying s + -13 = 11.489125293 Reorder the terms: -13 + s = 11.489125293 Solving -13 + s = 11.489125293 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + s = 11.489125293 + 13 Combine like terms: -13 + 13 = 0 0 + s = 11.489125293 + 13 s = 11.489125293 + 13 Combine like terms: 11.489125293 + 13 = 24.489125293 s = 24.489125293 Simplifying s = 24.489125293Subproblem 2
s + -13 = -11.489125293 Simplifying s + -13 = -11.489125293 Reorder the terms: -13 + s = -11.489125293 Solving -13 + s = -11.489125293 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + s = -11.489125293 + 13 Combine like terms: -13 + 13 = 0 0 + s = -11.489125293 + 13 s = -11.489125293 + 13 Combine like terms: -11.489125293 + 13 = 1.510874707 s = 1.510874707 Simplifying s = 1.510874707Solution
The solution to the problem is based on the solutions from the subproblems. s = {24.489125293, 1.510874707}Solution
s = {24.489125293, 1.510874707}
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