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Simplifying 2s2 + -32s = 56 Reorder the terms: -32s + 2s2 = 56 Solving -32s + 2s2 = 56 Solving for variable 's'. Reorder the terms: -56 + -32s + 2s2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -32s + 2s2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -16s + s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -16s + s2)' equal to zero and attempt to solve: Simplifying -28 + -16s + s2 = 0 Solving -28 + -16s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -16s + 28 + s2 = 0 + 28 Reorder the terms: -28 + 28 + -16s + s2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -16s + s2 = 0 + 28 -16s + s2 = 0 + 28 Combine like terms: 0 + 28 = 28 -16s + s2 = 28 The s term is -16s. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16s + 64 + s2 = 28 + 64 Reorder the terms: 64 + -16s + s2 = 28 + 64 Combine like terms: 28 + 64 = 92 64 + -16s + s2 = 92 Factor a perfect square on the left side: (s + -8)(s + -8) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (s + -8) equal to 9.591663047 and -9.591663047.Subproblem 1
s + -8 = 9.591663047 Simplifying s + -8 = 9.591663047 Reorder the terms: -8 + s = 9.591663047 Solving -8 + s = 9.591663047 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + s = 9.591663047 + 8 Combine like terms: -8 + 8 = 0 0 + s = 9.591663047 + 8 s = 9.591663047 + 8 Combine like terms: 9.591663047 + 8 = 17.591663047 s = 17.591663047 Simplifying s = 17.591663047Subproblem 2
s + -8 = -9.591663047 Simplifying s + -8 = -9.591663047 Reorder the terms: -8 + s = -9.591663047 Solving -8 + s = -9.591663047 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + s = -9.591663047 + 8 Combine like terms: -8 + 8 = 0 0 + s = -9.591663047 + 8 s = -9.591663047 + 8 Combine like terms: -9.591663047 + 8 = -1.591663047 s = -1.591663047 Simplifying s = -1.591663047Solution
The solution to the problem is based on the solutions from the subproblems. s = {17.591663047, -1.591663047}Solution
s = {17.591663047, -1.591663047}
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