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Simplifying (s + -4)(s + -5) = 9 Reorder the terms: (-4 + s)(s + -5) = 9 Reorder the terms: (-4 + s)(-5 + s) = 9 Multiply (-4 + s) * (-5 + s) (-4(-5 + s) + s(-5 + s)) = 9 ((-5 * -4 + s * -4) + s(-5 + s)) = 9 ((20 + -4s) + s(-5 + s)) = 9 (20 + -4s + (-5 * s + s * s)) = 9 (20 + -4s + (-5s + s2)) = 9 Combine like terms: -4s + -5s = -9s (20 + -9s + s2) = 9 Solving 20 + -9s + s2 = 9 Solving for variable 's'. Reorder the terms: 20 + -9 + -9s + s2 = 9 + -9 Combine like terms: 20 + -9 = 11 11 + -9s + s2 = 9 + -9 Combine like terms: 9 + -9 = 0 11 + -9s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -9s + -11 + s2 = 0 + -11 Reorder the terms: 11 + -11 + -9s + s2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -9s + s2 = 0 + -11 -9s + s2 = 0 + -11 Combine like terms: 0 + -11 = -11 -9s + s2 = -11 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 = -11 + 20.25 Reorder the terms: 20.25 + -9s + s2 = -11 + 20.25 Combine like terms: -11 + 20.25 = 9.25 20.25 + -9s + s2 = 9.25 Factor a perfect square on the left side: (s + -4.5)(s + -4.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (s + -4.5) equal to 3.041381265 and -3.041381265.Subproblem 1
s + -4.5 = 3.041381265 Simplifying s + -4.5 = 3.041381265 Reorder the terms: -4.5 + s = 3.041381265 Solving -4.5 + s = 3.041381265 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 = 3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + s = 3.041381265 + 4.5 s = 3.041381265 + 4.5 Combine like terms: 3.041381265 + 4.5 = 7.541381265 s = 7.541381265 Simplifying s = 7.541381265Subproblem 2
s + -4.5 = -3.041381265 Simplifying s + -4.5 = -3.041381265 Reorder the terms: -4.5 + s = -3.041381265 Solving -4.5 + s = -3.041381265 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 = -3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + s = -3.041381265 + 4.5 s = -3.041381265 + 4.5 Combine like terms: -3.041381265 + 4.5 = 1.458618735 s = 1.458618735 Simplifying s = 1.458618735Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.541381265, 1.458618735}
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