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Simplifying s(s + -3) = 38 Reorder the terms: s(-3 + s) = 38 (-3 * s + s * s) = 38 (-3s + s2) = 38 Solving -3s + s2 = 38 Solving for variable 's'. Reorder the terms: -38 + -3s + s2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -3s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -3s + 38 + s2 = 0 + 38 Reorder the terms: -38 + 38 + -3s + s2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -3s + s2 = 0 + 38 -3s + s2 = 0 + 38 Combine like terms: 0 + 38 = 38 -3s + s2 = 38 The s term is -3s. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3s + 2.25 + s2 = 38 + 2.25 Reorder the terms: 2.25 + -3s + s2 = 38 + 2.25 Combine like terms: 38 + 2.25 = 40.25 2.25 + -3s + s2 = 40.25 Factor a perfect square on the left side: (s + -1.5)(s + -1.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (s + -1.5) equal to 6.34428877 and -6.34428877.Subproblem 1
s + -1.5 = 6.34428877 Simplifying s + -1.5 = 6.34428877 Reorder the terms: -1.5 + s = 6.34428877 Solving -1.5 + s = 6.34428877 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + s = 6.34428877 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + s = 6.34428877 + 1.5 s = 6.34428877 + 1.5 Combine like terms: 6.34428877 + 1.5 = 7.84428877 s = 7.84428877 Simplifying s = 7.84428877Subproblem 2
s + -1.5 = -6.34428877 Simplifying s + -1.5 = -6.34428877 Reorder the terms: -1.5 + s = -6.34428877 Solving -1.5 + s = -6.34428877 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + s = -6.34428877 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + s = -6.34428877 + 1.5 s = -6.34428877 + 1.5 Combine like terms: -6.34428877 + 1.5 = -4.84428877 s = -4.84428877 Simplifying s = -4.84428877Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.84428877, -4.84428877}
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