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Simplifying 24 + -2s = 20s(2s + -3) Reorder the terms: 24 + -2s = 20s(-3 + 2s) 24 + -2s = (-3 * 20s + 2s * 20s) 24 + -2s = (-60s + 40s2) Solving 24 + -2s = -60s + 40s2 Solving for variable 's'. Combine like terms: -2s + 60s = 58s 24 + 58s + -40s2 = -60s + 40s2 + 60s + -40s2 Reorder the terms: 24 + 58s + -40s2 = -60s + 60s + 40s2 + -40s2 Combine like terms: -60s + 60s = 0 24 + 58s + -40s2 = 0 + 40s2 + -40s2 24 + 58s + -40s2 = 40s2 + -40s2 Combine like terms: 40s2 + -40s2 = 0 24 + 58s + -40s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 29s + -20s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 29s + -20s2)' equal to zero and attempt to solve: Simplifying 12 + 29s + -20s2 = 0 Solving 12 + 29s + -20s2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.6 + -1.45s + s2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.45s + 0.6 + s2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.45s + s2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.45s + s2 = 0.0 + 0.6 -1.45s + s2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -1.45s + s2 = 0.6 The s term is -1.45s. Take half its coefficient (-0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. -1.45s + 0.525625 + s2 = 0.6 + 0.525625 Reorder the terms: 0.525625 + -1.45s + s2 = 0.6 + 0.525625 Combine like terms: 0.6 + 0.525625 = 1.125625 0.525625 + -1.45s + s2 = 1.125625 Factor a perfect square on the left side: (s + -0.725)(s + -0.725) = 1.125625 Calculate the square root of the right side: 1.060954759 Break this problem into two subproblems by setting (s + -0.725) equal to 1.060954759 and -1.060954759.Subproblem 1
s + -0.725 = 1.060954759 Simplifying s + -0.725 = 1.060954759 Reorder the terms: -0.725 + s = 1.060954759 Solving -0.725 + s = 1.060954759 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.725' to each side of the equation. -0.725 + 0.725 + s = 1.060954759 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + s = 1.060954759 + 0.725 s = 1.060954759 + 0.725 Combine like terms: 1.060954759 + 0.725 = 1.785954759 s = 1.785954759 Simplifying s = 1.785954759Subproblem 2
s + -0.725 = -1.060954759 Simplifying s + -0.725 = -1.060954759 Reorder the terms: -0.725 + s = -1.060954759 Solving -0.725 + s = -1.060954759 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.725' to each side of the equation. -0.725 + 0.725 + s = -1.060954759 + 0.725 Combine like terms: -0.725 + 0.725 = 0.000 0.000 + s = -1.060954759 + 0.725 s = -1.060954759 + 0.725 Combine like terms: -1.060954759 + 0.725 = -0.335954759 s = -0.335954759 Simplifying s = -0.335954759Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.785954759, -0.335954759}Solution
s = {1.785954759, -0.335954759}
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