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Simplifying s2 + -10s + 14 = 0 Reorder the terms: 14 + -10s + s2 = 0 Solving 14 + -10s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10s + -14 + s2 = 0 + -14 Reorder the terms: 14 + -14 + -10s + s2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10s + s2 = 0 + -14 -10s + s2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10s + s2 = -14 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 = -14 + 25 Reorder the terms: 25 + -10s + s2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10s + s2 = 11 Factor a perfect square on the left side: (s + -5)(s + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (s + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
s + -5 = 3.31662479 Simplifying s + -5 = 3.31662479 Reorder the terms: -5 + s = 3.31662479 Solving -5 + s = 3.31662479 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 = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + s = 3.31662479 + 5 s = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 s = 8.31662479 Simplifying s = 8.31662479Subproblem 2
s + -5 = -3.31662479 Simplifying s + -5 = -3.31662479 Reorder the terms: -5 + s = -3.31662479 Solving -5 + s = -3.31662479 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 = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + s = -3.31662479 + 5 s = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 s = 1.68337521 Simplifying s = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.31662479, 1.68337521}
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