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Simplifying 6x2 + -6x + 3 + -4(x2 + 4x + 2) = 0 Reorder the terms: 6x2 + -6x + 3 + -4(2 + 4x + x2) = 0 6x2 + -6x + 3 + (2 * -4 + 4x * -4 + x2 * -4) = 0 6x2 + -6x + 3 + (-8 + -16x + -4x2) = 0 Reorder the terms: 3 + -8 + -6x + -16x + 6x2 + -4x2 = 0 Combine like terms: 3 + -8 = -5 -5 + -6x + -16x + 6x2 + -4x2 = 0 Combine like terms: -6x + -16x = -22x -5 + -22x + 6x2 + -4x2 = 0 Combine like terms: 6x2 + -4x2 = 2x2 -5 + -22x + 2x2 = 0 Solving -5 + -22x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -11x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -11x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -11x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -11x + x2 = 0 + 2.5 -11x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -11x + x2 = 2.5 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 = 2.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 2.5 + 30.25 Combine like terms: 2.5 + 30.25 = 32.75 30.25 + -11x + x2 = 32.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 32.75 Calculate the square root of the right side: 5.722761571 Break this problem into two subproblems by setting (x + -5.5) equal to 5.722761571 and -5.722761571.Subproblem 1
x + -5.5 = 5.722761571 Simplifying x + -5.5 = 5.722761571 Reorder the terms: -5.5 + x = 5.722761571 Solving -5.5 + x = 5.722761571 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 = 5.722761571 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.722761571 + 5.5 x = 5.722761571 + 5.5 Combine like terms: 5.722761571 + 5.5 = 11.222761571 x = 11.222761571 Simplifying x = 11.222761571Subproblem 2
x + -5.5 = -5.722761571 Simplifying x + -5.5 = -5.722761571 Reorder the terms: -5.5 + x = -5.722761571 Solving -5.5 + x = -5.722761571 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 = -5.722761571 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.722761571 + 5.5 x = -5.722761571 + 5.5 Combine like terms: -5.722761571 + 5.5 = -0.222761571 x = -0.222761571 Simplifying x = -0.222761571Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.222761571, -0.222761571}
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