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Simplifying 5x2 + -55x + -24 = 0 Reorder the terms: -24 + -55x + 5x2 = 0 Solving -24 + -55x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -11x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -11x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -11x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -11x + x2 = 0 + 4.8 -11x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -11x + x2 = 4.8 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 = 4.8 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 4.8 + 30.25 Combine like terms: 4.8 + 30.25 = 35.05 30.25 + -11x + x2 = 35.05 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 35.05 Calculate the square root of the right side: 5.920304046 Break this problem into two subproblems by setting (x + -5.5) equal to 5.920304046 and -5.920304046.Subproblem 1
x + -5.5 = 5.920304046 Simplifying x + -5.5 = 5.920304046 Reorder the terms: -5.5 + x = 5.920304046 Solving -5.5 + x = 5.920304046 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 = 5.920304046 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.920304046 + 5.5 x = 5.920304046 + 5.5 Combine like terms: 5.920304046 + 5.5 = 11.420304046 x = 11.420304046 Simplifying x = 11.420304046Subproblem 2
x + -5.5 = -5.920304046 Simplifying x + -5.5 = -5.920304046 Reorder the terms: -5.5 + x = -5.920304046 Solving -5.5 + x = -5.920304046 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 = -5.920304046 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.920304046 + 5.5 x = -5.920304046 + 5.5 Combine like terms: -5.920304046 + 5.5 = -0.420304046 x = -0.420304046 Simplifying x = -0.420304046Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.420304046, -0.420304046}
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