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Simplifying -2s2 + 28s + 63 = 0 Reorder the terms: 63 + 28s + -2s2 = 0 Solving 63 + 28s + -2s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -31.5 + -14s + s2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + -14s + 31.5 + s2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + -14s + s2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + -14s + s2 = 0 + 31.5 -14s + s2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 -14s + s2 = 31.5 The s term is -14s. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14s + 49 + s2 = 31.5 + 49 Reorder the terms: 49 + -14s + s2 = 31.5 + 49 Combine like terms: 31.5 + 49 = 80.5 49 + -14s + s2 = 80.5 Factor a perfect square on the left side: (s + -7)(s + -7) = 80.5 Calculate the square root of the right side: 8.972179222 Break this problem into two subproblems by setting (s + -7) equal to 8.972179222 and -8.972179222.Subproblem 1
s + -7 = 8.972179222 Simplifying s + -7 = 8.972179222 Reorder the terms: -7 + s = 8.972179222 Solving -7 + s = 8.972179222 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = 8.972179222 + 7 Combine like terms: -7 + 7 = 0 0 + s = 8.972179222 + 7 s = 8.972179222 + 7 Combine like terms: 8.972179222 + 7 = 15.972179222 s = 15.972179222 Simplifying s = 15.972179222Subproblem 2
s + -7 = -8.972179222 Simplifying s + -7 = -8.972179222 Reorder the terms: -7 + s = -8.972179222 Solving -7 + s = -8.972179222 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = -8.972179222 + 7 Combine like terms: -7 + 7 = 0 0 + s = -8.972179222 + 7 s = -8.972179222 + 7 Combine like terms: -8.972179222 + 7 = -1.972179222 s = -1.972179222 Simplifying s = -1.972179222Solution
The solution to the problem is based on the solutions from the subproblems. s = {15.972179222, -1.972179222}
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