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Simplifying s2 + -30s + 56 = 25 Reorder the terms: 56 + -30s + s2 = 25 Solving 56 + -30s + s2 = 25 Solving for variable 's'. Reorder the terms: 56 + -25 + -30s + s2 = 25 + -25 Combine like terms: 56 + -25 = 31 31 + -30s + s2 = 25 + -25 Combine like terms: 25 + -25 = 0 31 + -30s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -30s + -31 + s2 = 0 + -31 Reorder the terms: 31 + -31 + -30s + s2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -30s + s2 = 0 + -31 -30s + s2 = 0 + -31 Combine like terms: 0 + -31 = -31 -30s + s2 = -31 The s term is -30s. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30s + 225 + s2 = -31 + 225 Reorder the terms: 225 + -30s + s2 = -31 + 225 Combine like terms: -31 + 225 = 194 225 + -30s + s2 = 194 Factor a perfect square on the left side: (s + -15)(s + -15) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (s + -15) equal to 13.928388277 and -13.928388277.Subproblem 1
s + -15 = 13.928388277 Simplifying s + -15 = 13.928388277 Reorder the terms: -15 + s = 13.928388277 Solving -15 + s = 13.928388277 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s = 13.928388277 + 15 Combine like terms: -15 + 15 = 0 0 + s = 13.928388277 + 15 s = 13.928388277 + 15 Combine like terms: 13.928388277 + 15 = 28.928388277 s = 28.928388277 Simplifying s = 28.928388277Subproblem 2
s + -15 = -13.928388277 Simplifying s + -15 = -13.928388277 Reorder the terms: -15 + s = -13.928388277 Solving -15 + s = -13.928388277 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + s = -13.928388277 + 15 Combine like terms: -15 + 15 = 0 0 + s = -13.928388277 + 15 s = -13.928388277 + 15 Combine like terms: -13.928388277 + 15 = 1.071611723 s = 1.071611723 Simplifying s = 1.071611723Solution
The solution to the problem is based on the solutions from the subproblems. s = {28.928388277, 1.071611723}
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