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Simplifying 5s(s + -11) = 4 Reorder the terms: 5s(-11 + s) = 4 (-11 * 5s + s * 5s) = 4 (-55s + 5s2) = 4 Solving -55s + 5s2 = 4 Solving for variable 's'. Reorder the terms: -4 + -55s + 5s2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -55s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -11s + s2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -11s + 0.8 + s2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -11s + s2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -11s + s2 = 0 + 0.8 -11s + s2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -11s + s2 = 0.8 The s term is -11s. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11s + 30.25 + s2 = 0.8 + 30.25 Reorder the terms: 30.25 + -11s + s2 = 0.8 + 30.25 Combine like terms: 0.8 + 30.25 = 31.05 30.25 + -11s + s2 = 31.05 Factor a perfect square on the left side: (s + -5.5)(s + -5.5) = 31.05 Calculate the square root of the right side: 5.572252686 Break this problem into two subproblems by setting (s + -5.5) equal to 5.572252686 and -5.572252686.Subproblem 1
s + -5.5 = 5.572252686 Simplifying s + -5.5 = 5.572252686 Reorder the terms: -5.5 + s = 5.572252686 Solving -5.5 + s = 5.572252686 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + s = 5.572252686 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + s = 5.572252686 + 5.5 s = 5.572252686 + 5.5 Combine like terms: 5.572252686 + 5.5 = 11.072252686 s = 11.072252686 Simplifying s = 11.072252686Subproblem 2
s + -5.5 = -5.572252686 Simplifying s + -5.5 = -5.572252686 Reorder the terms: -5.5 + s = -5.572252686 Solving -5.5 + s = -5.572252686 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + s = -5.572252686 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + s = -5.572252686 + 5.5 s = -5.572252686 + 5.5 Combine like terms: -5.572252686 + 5.5 = -0.072252686 s = -0.072252686 Simplifying s = -0.072252686Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.072252686, -0.072252686}
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