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Simplifying s(s + -9) = -15 Reorder the terms: s(-9 + s) = -15 (-9 * s + s * s) = -15 (-9s + s2) = -15 Solving -9s + s2 = -15 Solving for variable 's'. Reorder the terms: 15 + -9s + s2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -9s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -9s + -15 + s2 = 0 + -15 Reorder the terms: 15 + -15 + -9s + s2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -9s + s2 = 0 + -15 -9s + s2 = 0 + -15 Combine like terms: 0 + -15 = -15 -9s + s2 = -15 The s term is -9s. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9s + 20.25 + s2 = -15 + 20.25 Reorder the terms: 20.25 + -9s + s2 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + -9s + s2 = 5.25 Factor a perfect square on the left side: (s + -4.5)(s + -4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (s + -4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
s + -4.5 = 2.291287847 Simplifying s + -4.5 = 2.291287847 Reorder the terms: -4.5 + s = 2.291287847 Solving -4.5 + s = 2.291287847 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + s = 2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + s = 2.291287847 + 4.5 s = 2.291287847 + 4.5 Combine like terms: 2.291287847 + 4.5 = 6.791287847 s = 6.791287847 Simplifying s = 6.791287847Subproblem 2
s + -4.5 = -2.291287847 Simplifying s + -4.5 = -2.291287847 Reorder the terms: -4.5 + s = -2.291287847 Solving -4.5 + s = -2.291287847 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + s = -2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + s = -2.291287847 + 4.5 s = -2.291287847 + 4.5 Combine like terms: -2.291287847 + 4.5 = 2.208712153 s = 2.208712153 Simplifying s = 2.208712153Solution
The solution to the problem is based on the solutions from the subproblems. s = {6.791287847, 2.208712153}
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