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Simplifying 4x2 + -24x + -11 = 0 Reorder the terms: -11 + -24x + 4x2 = 0 Solving -11 + -24x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -6x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -6x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -6x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -6x + x2 = 0 + 2.75 -6x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -6x + x2 = 2.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2.75 + 9 Reorder the terms: 9 + -6x + x2 = 2.75 + 9 Combine like terms: 2.75 + 9 = 11.75 9 + -6x + x2 = 11.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + -3) equal to 3.4278273 and -3.4278273.Subproblem 1
x + -3 = 3.4278273 Simplifying x + -3 = 3.4278273 Reorder the terms: -3 + x = 3.4278273 Solving -3 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.4278273 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.4278273 + 3 x = 3.4278273 + 3 Combine like terms: 3.4278273 + 3 = 6.4278273 x = 6.4278273 Simplifying x = 6.4278273Subproblem 2
x + -3 = -3.4278273 Simplifying x + -3 = -3.4278273 Reorder the terms: -3 + x = -3.4278273 Solving -3 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.4278273 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.4278273 + 3 x = -3.4278273 + 3 Combine like terms: -3.4278273 + 3 = -0.4278273 x = -0.4278273 Simplifying x = -0.4278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.4278273, -0.4278273}
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