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Simplifying s2 + -4s + -33 = 0 Reorder the terms: -33 + -4s + s2 = 0 Solving -33 + -4s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -4s + 33 + s2 = 0 + 33 Reorder the terms: -33 + 33 + -4s + s2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -4s + s2 = 0 + 33 -4s + s2 = 0 + 33 Combine like terms: 0 + 33 = 33 -4s + s2 = 33 The s term is -4s. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4s + 4 + s2 = 33 + 4 Reorder the terms: 4 + -4s + s2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + -4s + s2 = 37 Factor a perfect square on the left side: (s + -2)(s + -2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (s + -2) equal to 6.08276253 and -6.08276253.Subproblem 1
s + -2 = 6.08276253 Simplifying s + -2 = 6.08276253 Reorder the terms: -2 + s = 6.08276253 Solving -2 + s = 6.08276253 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = 6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + s = 6.08276253 + 2 s = 6.08276253 + 2 Combine like terms: 6.08276253 + 2 = 8.08276253 s = 8.08276253 Simplifying s = 8.08276253Subproblem 2
s + -2 = -6.08276253 Simplifying s + -2 = -6.08276253 Reorder the terms: -2 + s = -6.08276253 Solving -2 + s = -6.08276253 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = -6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + s = -6.08276253 + 2 s = -6.08276253 + 2 Combine like terms: -6.08276253 + 2 = -4.08276253 s = -4.08276253 Simplifying s = -4.08276253Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.08276253, -4.08276253}
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