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Simplifying (2s + 2)(s + 3) = 36 Reorder the terms: (2 + 2s)(s + 3) = 36 Reorder the terms: (2 + 2s)(3 + s) = 36 Multiply (2 + 2s) * (3 + s) (2(3 + s) + 2s * (3 + s)) = 36 ((3 * 2 + s * 2) + 2s * (3 + s)) = 36 ((6 + 2s) + 2s * (3 + s)) = 36 (6 + 2s + (3 * 2s + s * 2s)) = 36 (6 + 2s + (6s + 2s2)) = 36 Combine like terms: 2s + 6s = 8s (6 + 8s + 2s2) = 36 Solving 6 + 8s + 2s2 = 36 Solving for variable 's'. Reorder the terms: 6 + -36 + 8s + 2s2 = 36 + -36 Combine like terms: 6 + -36 = -30 -30 + 8s + 2s2 = 36 + -36 Combine like terms: 36 + -36 = 0 -30 + 8s + 2s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 4s + s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 4s + s2)' equal to zero and attempt to solve: Simplifying -15 + 4s + s2 = 0 Solving -15 + 4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 4s + 15 + s2 = 0 + 15 Reorder the terms: -15 + 15 + 4s + s2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4s + s2 = 0 + 15 4s + s2 = 0 + 15 Combine like terms: 0 + 15 = 15 4s + s2 = 15 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = 15 + 4 Reorder the terms: 4 + 4s + s2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4s + s2 = 19 Factor a perfect square on the left side: (s + 2)(s + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (s + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
s + 2 = 4.358898944 Simplifying s + 2 = 4.358898944 Reorder the terms: 2 + s = 4.358898944 Solving 2 + s = 4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + s = 4.358898944 + -2 s = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 s = 2.358898944 Simplifying s = 2.358898944Subproblem 2
s + 2 = -4.358898944 Simplifying s + 2 = -4.358898944 Reorder the terms: 2 + s = -4.358898944 Solving 2 + s = -4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + s = -4.358898944 + -2 s = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 s = -6.358898944 Simplifying s = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.358898944, -6.358898944}Solution
s = {2.358898944, -6.358898944}
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