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Simplifying s2 + -21 + 3 = s Reorder the terms: -21 + 3 + s2 = s Combine like terms: -21 + 3 = -18 -18 + s2 = s Solving -18 + s2 = s Solving for variable 's'. Reorder the terms: -18 + -1s + s2 = s + -1s Combine like terms: s + -1s = 0 -18 + -1s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -1s + 18 + s2 = 0 + 18 Reorder the terms: -18 + 18 + -1s + s2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1s + s2 = 0 + 18 -1s + s2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1s + s2 = 18 The s term is -1s. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1s + 0.25 + s2 = 18 + 0.25 Reorder the terms: 0.25 + -1s + s2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + -1s + s2 = 18.25 Factor a perfect square on the left side: (s + -0.5)(s + -0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (s + -0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
s + -0.5 = 4.272001873 Simplifying s + -0.5 = 4.272001873 Reorder the terms: -0.5 + s = 4.272001873 Solving -0.5 + s = 4.272001873 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = 4.272001873 + 0.5 s = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 s = 4.772001873 Simplifying s = 4.772001873Subproblem 2
s + -0.5 = -4.272001873 Simplifying s + -0.5 = -4.272001873 Reorder the terms: -0.5 + s = -4.272001873 Solving -0.5 + s = -4.272001873 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = -4.272001873 + 0.5 s = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 s = -3.772001873 Simplifying s = -3.772001873Solution
The solution to the problem is based on the solutions from the subproblems. s = {4.772001873, -3.772001873}
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