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Simplifying 8s2 + -480s + -2552 = 0 Reorder the terms: -2552 + -480s + 8s2 = 0 Solving -2552 + -480s + 8s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '8'. 8(-319 + -60s + s2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-319 + -60s + s2)' equal to zero and attempt to solve: Simplifying -319 + -60s + s2 = 0 Solving -319 + -60s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '319' to each side of the equation. -319 + -60s + 319 + s2 = 0 + 319 Reorder the terms: -319 + 319 + -60s + s2 = 0 + 319 Combine like terms: -319 + 319 = 0 0 + -60s + s2 = 0 + 319 -60s + s2 = 0 + 319 Combine like terms: 0 + 319 = 319 -60s + s2 = 319 The s term is -60s. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60s + 900 + s2 = 319 + 900 Reorder the terms: 900 + -60s + s2 = 319 + 900 Combine like terms: 319 + 900 = 1219 900 + -60s + s2 = 1219 Factor a perfect square on the left side: (s + -30)(s + -30) = 1219 Calculate the square root of the right side: 34.9141805 Break this problem into two subproblems by setting (s + -30) equal to 34.9141805 and -34.9141805.Subproblem 1
s + -30 = 34.9141805 Simplifying s + -30 = 34.9141805 Reorder the terms: -30 + s = 34.9141805 Solving -30 + s = 34.9141805 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + s = 34.9141805 + 30 Combine like terms: -30 + 30 = 0 0 + s = 34.9141805 + 30 s = 34.9141805 + 30 Combine like terms: 34.9141805 + 30 = 64.9141805 s = 64.9141805 Simplifying s = 64.9141805Subproblem 2
s + -30 = -34.9141805 Simplifying s + -30 = -34.9141805 Reorder the terms: -30 + s = -34.9141805 Solving -30 + s = -34.9141805 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + s = -34.9141805 + 30 Combine like terms: -30 + 30 = 0 0 + s = -34.9141805 + 30 s = -34.9141805 + 30 Combine like terms: -34.9141805 + 30 = -4.9141805 s = -4.9141805 Simplifying s = -4.9141805Solution
The solution to the problem is based on the solutions from the subproblems. s = {64.9141805, -4.9141805}Solution
s = {64.9141805, -4.9141805}
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