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Simplifying s2 = 4s + 6 Reorder the terms: s2 = 6 + 4s Solving s2 = 6 + 4s Solving for variable 's'. Reorder the terms: -6 + -4s + s2 = 6 + 4s + -6 + -4s Reorder the terms: -6 + -4s + s2 = 6 + -6 + 4s + -4s Combine like terms: 6 + -6 = 0 -6 + -4s + s2 = 0 + 4s + -4s -6 + -4s + s2 = 4s + -4s Combine like terms: 4s + -4s = 0 -6 + -4s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -4s + 6 + s2 = 0 + 6 Reorder the terms: -6 + 6 + -4s + s2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4s + s2 = 0 + 6 -4s + s2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4s + s2 = 6 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 = 6 + 4 Reorder the terms: 4 + -4s + s2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4s + s2 = 10 Factor a perfect square on the left side: (s + -2)(s + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (s + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
s + -2 = 3.16227766 Simplifying s + -2 = 3.16227766 Reorder the terms: -2 + s = 3.16227766 Solving -2 + s = 3.16227766 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 = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + s = 3.16227766 + 2 s = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 s = 5.16227766 Simplifying s = 5.16227766Subproblem 2
s + -2 = -3.16227766 Simplifying s + -2 = -3.16227766 Reorder the terms: -2 + s = -3.16227766 Solving -2 + s = -3.16227766 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 = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + s = -3.16227766 + 2 s = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 s = -1.16227766 Simplifying s = -1.16227766Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.16227766, -1.16227766}
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