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Simplifying s2 + 10s = 21 Reorder the terms: 10s + s2 = 21 Solving 10s + s2 = 21 Solving for variable 's'. Reorder the terms: -21 + 10s + s2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 10s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 10s + 21 + s2 = 0 + 21 Reorder the terms: -21 + 21 + 10s + s2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 10s + s2 = 0 + 21 10s + s2 = 0 + 21 Combine like terms: 0 + 21 = 21 10s + s2 = 21 The s term is 10s. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10s + 25 + s2 = 21 + 25 Reorder the terms: 25 + 10s + s2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + 10s + s2 = 46 Factor a perfect square on the left side: (s + 5)(s + 5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (s + 5) equal to 6.782329983 and -6.782329983.Subproblem 1
s + 5 = 6.782329983 Simplifying s + 5 = 6.782329983 Reorder the terms: 5 + s = 6.782329983 Solving 5 + s = 6.782329983 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = 6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + s = 6.782329983 + -5 s = 6.782329983 + -5 Combine like terms: 6.782329983 + -5 = 1.782329983 s = 1.782329983 Simplifying s = 1.782329983Subproblem 2
s + 5 = -6.782329983 Simplifying s + 5 = -6.782329983 Reorder the terms: 5 + s = -6.782329983 Solving 5 + s = -6.782329983 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + s = -6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + s = -6.782329983 + -5 s = -6.782329983 + -5 Combine like terms: -6.782329983 + -5 = -11.782329983 s = -11.782329983 Simplifying s = -11.782329983Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.782329983, -11.782329983}
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