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Simplifying s2 + 10s + -13 = 0 Reorder the terms: -13 + 10s + s2 = 0 Solving -13 + 10s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 10s + 13 + s2 = 0 + 13 Reorder the terms: -13 + 13 + 10s + s2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 10s + s2 = 0 + 13 10s + s2 = 0 + 13 Combine like terms: 0 + 13 = 13 10s + s2 = 13 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 = 13 + 25 Reorder the terms: 25 + 10s + s2 = 13 + 25 Combine like terms: 13 + 25 = 38 25 + 10s + s2 = 38 Factor a perfect square on the left side: (s + 5)(s + 5) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (s + 5) equal to 6.164414003 and -6.164414003.Subproblem 1
s + 5 = 6.164414003 Simplifying s + 5 = 6.164414003 Reorder the terms: 5 + s = 6.164414003 Solving 5 + s = 6.164414003 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 = 6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + s = 6.164414003 + -5 s = 6.164414003 + -5 Combine like terms: 6.164414003 + -5 = 1.164414003 s = 1.164414003 Simplifying s = 1.164414003Subproblem 2
s + 5 = -6.164414003 Simplifying s + 5 = -6.164414003 Reorder the terms: 5 + s = -6.164414003 Solving 5 + s = -6.164414003 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 = -6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + s = -6.164414003 + -5 s = -6.164414003 + -5 Combine like terms: -6.164414003 + -5 = -11.164414003 s = -11.164414003 Simplifying s = -11.164414003Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.164414003, -11.164414003}
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