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Simplifying 98s2 + 648s + -5880 = 0 Reorder the terms: -5880 + 648s + 98s2 = 0 Solving -5880 + 648s + 98s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2940 + 324s + 49s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2940 + 324s + 49s2)' equal to zero and attempt to solve: Simplifying -2940 + 324s + 49s2 = 0 Solving -2940 + 324s + 49s2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -60 + 6.612244898s + s2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 6.612244898s + 60 + s2 = 0 + 60 Reorder the terms: -60 + 60 + 6.612244898s + s2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 6.612244898s + s2 = 0 + 60 6.612244898s + s2 = 0 + 60 Combine like terms: 0 + 60 = 60 6.612244898s + s2 = 60 The s term is 6.612244898s. Take half its coefficient (3.306122449). Square it (10.93044565) and add it to both sides. Add '10.93044565' to each side of the equation. 6.612244898s + 10.93044565 + s2 = 60 + 10.93044565 Reorder the terms: 10.93044565 + 6.612244898s + s2 = 60 + 10.93044565 Combine like terms: 60 + 10.93044565 = 70.93044565 10.93044565 + 6.612244898s + s2 = 70.93044565 Factor a perfect square on the left side: (s + 3.306122449)(s + 3.306122449) = 70.93044565 Calculate the square root of the right side: 8.422021471 Break this problem into two subproblems by setting (s + 3.306122449) equal to 8.422021471 and -8.422021471.Subproblem 1
s + 3.306122449 = 8.422021471 Simplifying s + 3.306122449 = 8.422021471 Reorder the terms: 3.306122449 + s = 8.422021471 Solving 3.306122449 + s = 8.422021471 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.306122449' to each side of the equation. 3.306122449 + -3.306122449 + s = 8.422021471 + -3.306122449 Combine like terms: 3.306122449 + -3.306122449 = 0.000000000 0.000000000 + s = 8.422021471 + -3.306122449 s = 8.422021471 + -3.306122449 Combine like terms: 8.422021471 + -3.306122449 = 5.115899022 s = 5.115899022 Simplifying s = 5.115899022Subproblem 2
s + 3.306122449 = -8.422021471 Simplifying s + 3.306122449 = -8.422021471 Reorder the terms: 3.306122449 + s = -8.422021471 Solving 3.306122449 + s = -8.422021471 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.306122449' to each side of the equation. 3.306122449 + -3.306122449 + s = -8.422021471 + -3.306122449 Combine like terms: 3.306122449 + -3.306122449 = 0.000000000 0.000000000 + s = -8.422021471 + -3.306122449 s = -8.422021471 + -3.306122449 Combine like terms: -8.422021471 + -3.306122449 = -11.72814392 s = -11.72814392 Simplifying s = -11.72814392Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.115899022, -11.72814392}Solution
s = {5.115899022, -11.72814392}
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