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Simplifying s2 + 28s = 15 Reorder the terms: 28s + s2 = 15 Solving 28s + s2 = 15 Solving for variable 's'. Reorder the terms: -15 + 28s + s2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 28s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 28s + 15 + s2 = 0 + 15 Reorder the terms: -15 + 15 + 28s + s2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 28s + s2 = 0 + 15 28s + s2 = 0 + 15 Combine like terms: 0 + 15 = 15 28s + s2 = 15 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 = 15 + 196 Reorder the terms: 196 + 28s + s2 = 15 + 196 Combine like terms: 15 + 196 = 211 196 + 28s + s2 = 211 Factor a perfect square on the left side: (s + 14)(s + 14) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (s + 14) equal to 14.525839046 and -14.525839046.Subproblem 1
s + 14 = 14.525839046 Simplifying s + 14 = 14.525839046 Reorder the terms: 14 + s = 14.525839046 Solving 14 + s = 14.525839046 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 = 14.525839046 + -14 Combine like terms: 14 + -14 = 0 0 + s = 14.525839046 + -14 s = 14.525839046 + -14 Combine like terms: 14.525839046 + -14 = 0.525839046 s = 0.525839046 Simplifying s = 0.525839046Subproblem 2
s + 14 = -14.525839046 Simplifying s + 14 = -14.525839046 Reorder the terms: 14 + s = -14.525839046 Solving 14 + s = -14.525839046 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 = -14.525839046 + -14 Combine like terms: 14 + -14 = 0 0 + s = -14.525839046 + -14 s = -14.525839046 + -14 Combine like terms: -14.525839046 + -14 = -28.525839046 s = -28.525839046 Simplifying s = -28.525839046Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.525839046, -28.525839046}
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