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Simplifying 5.5x2 + x + -1.1 = 4x(3 + -1x) Reorder the terms: -1.1 + x + 5.5x2 = 4x(3 + -1x) -1.1 + x + 5.5x2 = (3 * 4x + -1x * 4x) -1.1 + x + 5.5x2 = (12x + -4x2) Solving -1.1 + x + 5.5x2 = 12x + -4x2 Solving for variable 'x'. Reorder the terms: -1.1 + x + -12x + 5.5x2 + 4x2 = 12x + -4x2 + -12x + 4x2 Combine like terms: x + -12x = -11x -1.1 + -11x + 5.5x2 + 4x2 = 12x + -4x2 + -12x + 4x2 Combine like terms: 5.5x2 + 4x2 = 9.5x2 -1.1 + -11x + 9.5x2 = 12x + -4x2 + -12x + 4x2 Reorder the terms: -1.1 + -11x + 9.5x2 = 12x + -12x + -4x2 + 4x2 Combine like terms: 12x + -12x = 0 -1.1 + -11x + 9.5x2 = 0 + -4x2 + 4x2 -1.1 + -11x + 9.5x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -1.1 + -11x + 9.5x2 = 0 Begin completing the square. Divide all terms by 9.5 the coefficient of the squared term: Divide each side by '9.5'. -0.1157894737 + -1.157894737x + x2 = 0 Move the constant term to the right: Add '0.1157894737' to each side of the equation. -0.1157894737 + -1.157894737x + 0.1157894737 + x2 = 0 + 0.1157894737 Reorder the terms: -0.1157894737 + 0.1157894737 + -1.157894737x + x2 = 0 + 0.1157894737 Combine like terms: -0.1157894737 + 0.1157894737 = 0.0000000000 0.0000000000 + -1.157894737x + x2 = 0 + 0.1157894737 -1.157894737x + x2 = 0 + 0.1157894737 Combine like terms: 0 + 0.1157894737 = 0.1157894737 -1.157894737x + x2 = 0.1157894737 The x term is -1.157894737x. Take half its coefficient (-0.5789473685). Square it (0.3351800555) and add it to both sides. Add '0.3351800555' to each side of the equation. -1.157894737x + 0.3351800555 + x2 = 0.1157894737 + 0.3351800555 Reorder the terms: 0.3351800555 + -1.157894737x + x2 = 0.1157894737 + 0.3351800555 Combine like terms: 0.1157894737 + 0.3351800555 = 0.4509695292 0.3351800555 + -1.157894737x + x2 = 0.4509695292 Factor a perfect square on the left side: (x + -0.5789473685)(x + -0.5789473685) = 0.4509695292 Calculate the square root of the right side: 0.671542649 Break this problem into two subproblems by setting (x + -0.5789473685) equal to 0.671542649 and -0.671542649.Subproblem 1
x + -0.5789473685 = 0.671542649 Simplifying x + -0.5789473685 = 0.671542649 Reorder the terms: -0.5789473685 + x = 0.671542649 Solving -0.5789473685 + x = 0.671542649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5789473685' to each side of the equation. -0.5789473685 + 0.5789473685 + x = 0.671542649 + 0.5789473685 Combine like terms: -0.5789473685 + 0.5789473685 = 0.0000000000 0.0000000000 + x = 0.671542649 + 0.5789473685 x = 0.671542649 + 0.5789473685 Combine like terms: 0.671542649 + 0.5789473685 = 1.2504900175 x = 1.2504900175 Simplifying x = 1.2504900175Subproblem 2
x + -0.5789473685 = -0.671542649 Simplifying x + -0.5789473685 = -0.671542649 Reorder the terms: -0.5789473685 + x = -0.671542649 Solving -0.5789473685 + x = -0.671542649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5789473685' to each side of the equation. -0.5789473685 + 0.5789473685 + x = -0.671542649 + 0.5789473685 Combine like terms: -0.5789473685 + 0.5789473685 = 0.0000000000 0.0000000000 + x = -0.671542649 + 0.5789473685 x = -0.671542649 + 0.5789473685 Combine like terms: -0.671542649 + 0.5789473685 = -0.0925952805 x = -0.0925952805 Simplifying x = -0.0925952805Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2504900175, -0.0925952805}
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