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Simplifying 5x(x + -11) = 8 Reorder the terms: 5x(-11 + x) = 8 (-11 * 5x + x * 5x) = 8 (-55x + 5x2) = 8 Solving -55x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -55x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -55x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -11x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -11x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -11x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -11x + x2 = 0 + 1.6 -11x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -11x + x2 = 1.6 The x term is -11x. 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. -11x + 30.25 + x2 = 1.6 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 1.6 + 30.25 Combine like terms: 1.6 + 30.25 = 31.85 30.25 + -11x + x2 = 31.85 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 31.85 Calculate the square root of the right side: 5.643580424 Break this problem into two subproblems by setting (x + -5.5) equal to 5.643580424 and -5.643580424.Subproblem 1
x + -5.5 = 5.643580424 Simplifying x + -5.5 = 5.643580424 Reorder the terms: -5.5 + x = 5.643580424 Solving -5.5 + x = 5.643580424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.643580424 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.643580424 + 5.5 x = 5.643580424 + 5.5 Combine like terms: 5.643580424 + 5.5 = 11.143580424 x = 11.143580424 Simplifying x = 11.143580424Subproblem 2
x + -5.5 = -5.643580424 Simplifying x + -5.5 = -5.643580424 Reorder the terms: -5.5 + x = -5.643580424 Solving -5.5 + x = -5.643580424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.643580424 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.643580424 + 5.5 x = -5.643580424 + 5.5 Combine like terms: -5.643580424 + 5.5 = -0.143580424 x = -0.143580424 Simplifying x = -0.143580424Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.143580424, -0.143580424}
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