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Simplifying s2 + 10s = 10 Reorder the terms: 10s + s2 = 10 Solving 10s + s2 = 10 Solving for variable 's'. Reorder the terms: -10 + 10s + s2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 10s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 10s + 10 + s2 = 0 + 10 Reorder the terms: -10 + 10 + 10s + s2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10s + s2 = 0 + 10 10s + s2 = 0 + 10 Combine like terms: 0 + 10 = 10 10s + s2 = 10 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 = 10 + 25 Reorder the terms: 25 + 10s + s2 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + 10s + s2 = 35 Factor a perfect square on the left side: (s + 5)(s + 5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (s + 5) equal to 5.916079783 and -5.916079783.Subproblem 1
s + 5 = 5.916079783 Simplifying s + 5 = 5.916079783 Reorder the terms: 5 + s = 5.916079783 Solving 5 + s = 5.916079783 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 = 5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + s = 5.916079783 + -5 s = 5.916079783 + -5 Combine like terms: 5.916079783 + -5 = 0.916079783 s = 0.916079783 Simplifying s = 0.916079783Subproblem 2
s + 5 = -5.916079783 Simplifying s + 5 = -5.916079783 Reorder the terms: 5 + s = -5.916079783 Solving 5 + s = -5.916079783 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 = -5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + s = -5.916079783 + -5 s = -5.916079783 + -5 Combine like terms: -5.916079783 + -5 = -10.916079783 s = -10.916079783 Simplifying s = -10.916079783Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.916079783, -10.916079783}
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