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Simplifying -2s2 + -56s + -2 = 0 Reorder the terms: -2 + -56s + -2s2 = 0 Solving -2 + -56s + -2s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 28s + s2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + 28s + s2)' equal to zero and attempt to solve: Simplifying 1 + 28s + s2 = 0 Solving 1 + 28s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 28s + -1 + s2 = 0 + -1 Reorder the terms: 1 + -1 + 28s + s2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 28s + s2 = 0 + -1 28s + s2 = 0 + -1 Combine like terms: 0 + -1 = -1 28s + s2 = -1 The s term is 28s. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28s + 196 + s2 = -1 + 196 Reorder the terms: 196 + 28s + s2 = -1 + 196 Combine like terms: -1 + 196 = 195 196 + 28s + s2 = 195 Factor a perfect square on the left side: (s + 14)(s + 14) = 195 Calculate the square root of the right side: 13.964240044 Break this problem into two subproblems by setting (s + 14) equal to 13.964240044 and -13.964240044.Subproblem 1
s + 14 = 13.964240044 Simplifying s + 14 = 13.964240044 Reorder the terms: 14 + s = 13.964240044 Solving 14 + s = 13.964240044 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + s = 13.964240044 + -14 Combine like terms: 14 + -14 = 0 0 + s = 13.964240044 + -14 s = 13.964240044 + -14 Combine like terms: 13.964240044 + -14 = -0.035759956 s = -0.035759956 Simplifying s = -0.035759956Subproblem 2
s + 14 = -13.964240044 Simplifying s + 14 = -13.964240044 Reorder the terms: 14 + s = -13.964240044 Solving 14 + s = -13.964240044 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + s = -13.964240044 + -14 Combine like terms: 14 + -14 = 0 0 + s = -13.964240044 + -14 s = -13.964240044 + -14 Combine like terms: -13.964240044 + -14 = -27.964240044 s = -27.964240044 Simplifying s = -27.964240044Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.035759956, -27.964240044}Solution
s = {-0.035759956, -27.964240044}
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