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Simplifying 24s + 60 = 2s2 + 10 Reorder the terms: 60 + 24s = 2s2 + 10 Reorder the terms: 60 + 24s = 10 + 2s2 Solving 60 + 24s = 10 + 2s2 Solving for variable 's'. Reorder the terms: 60 + -10 + 24s + -2s2 = 10 + 2s2 + -10 + -2s2 Combine like terms: 60 + -10 = 50 50 + 24s + -2s2 = 10 + 2s2 + -10 + -2s2 Reorder the terms: 50 + 24s + -2s2 = 10 + -10 + 2s2 + -2s2 Combine like terms: 10 + -10 = 0 50 + 24s + -2s2 = 0 + 2s2 + -2s2 50 + 24s + -2s2 = 2s2 + -2s2 Combine like terms: 2s2 + -2s2 = 0 50 + 24s + -2s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 12s + -1s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 12s + -1s2)' equal to zero and attempt to solve: Simplifying 25 + 12s + -1s2 = 0 Solving 25 + 12s + -1s2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -12s + s2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -12s + 25 + s2 = 0 + 25 Reorder the terms: -25 + 25 + -12s + s2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -12s + s2 = 0 + 25 -12s + s2 = 0 + 25 Combine like terms: 0 + 25 = 25 -12s + s2 = 25 The s term is -12s. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12s + 36 + s2 = 25 + 36 Reorder the terms: 36 + -12s + s2 = 25 + 36 Combine like terms: 25 + 36 = 61 36 + -12s + s2 = 61 Factor a perfect square on the left side: (s + -6)(s + -6) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (s + -6) equal to 7.810249676 and -7.810249676.Subproblem 1
s + -6 = 7.810249676 Simplifying s + -6 = 7.810249676 Reorder the terms: -6 + s = 7.810249676 Solving -6 + s = 7.810249676 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = 7.810249676 + 6 Combine like terms: -6 + 6 = 0 0 + s = 7.810249676 + 6 s = 7.810249676 + 6 Combine like terms: 7.810249676 + 6 = 13.810249676 s = 13.810249676 Simplifying s = 13.810249676Subproblem 2
s + -6 = -7.810249676 Simplifying s + -6 = -7.810249676 Reorder the terms: -6 + s = -7.810249676 Solving -6 + s = -7.810249676 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = -7.810249676 + 6 Combine like terms: -6 + 6 = 0 0 + s = -7.810249676 + 6 s = -7.810249676 + 6 Combine like terms: -7.810249676 + 6 = -1.810249676 s = -1.810249676 Simplifying s = -1.810249676Solution
The solution to the problem is based on the solutions from the subproblems. s = {13.810249676, -1.810249676}Solution
s = {13.810249676, -1.810249676}
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