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Simplifying s2 + 2s + -10 = 0 Reorder the terms: -10 + 2s + s2 = 0 Solving -10 + 2s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2s + 10 + s2 = 0 + 10 Reorder the terms: -10 + 10 + 2s + s2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2s + s2 = 0 + 10 2s + s2 = 0 + 10 Combine like terms: 0 + 10 = 10 2s + s2 = 10 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 10 + 1 Reorder the terms: 1 + 2s + s2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2s + s2 = 11 Factor a perfect square on the left side: (s + 1)(s + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (s + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
s + 1 = 3.31662479 Simplifying s + 1 = 3.31662479 Reorder the terms: 1 + s = 3.31662479 Solving 1 + s = 3.31662479 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + s = 3.31662479 + -1 s = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 s = 2.31662479 Simplifying s = 2.31662479Subproblem 2
s + 1 = -3.31662479 Simplifying s + 1 = -3.31662479 Reorder the terms: 1 + s = -3.31662479 Solving 1 + s = -3.31662479 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + s = -3.31662479 + -1 s = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 s = -4.31662479 Simplifying s = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.31662479, -4.31662479}
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