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Simplifying 3x2 + -3.2x + -2.4 = 0 Reorder the terms: -2.4 + -3.2x + 3x2 = 0 Solving -2.4 + -3.2x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.8 + -1.066666667x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.066666667x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.066666667x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.066666667x + x2 = 0 + 0.8 -1.066666667x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.066666667x + x2 = 0.8 The x term is -1.066666667x. Take half its coefficient (-0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. -1.066666667x + 0.2844444446 + x2 = 0.8 + 0.2844444446 Reorder the terms: 0.2844444446 + -1.066666667x + x2 = 0.8 + 0.2844444446 Combine like terms: 0.8 + 0.2844444446 = 1.0844444446 0.2844444446 + -1.066666667x + x2 = 1.0844444446 Factor a perfect square on the left side: (x + -0.5333333335)(x + -0.5333333335) = 1.0844444446 Calculate the square root of the right side: 1.041366624 Break this problem into two subproblems by setting (x + -0.5333333335) equal to 1.041366624 and -1.041366624.Subproblem 1
x + -0.5333333335 = 1.041366624 Simplifying x + -0.5333333335 = 1.041366624 Reorder the terms: -0.5333333335 + x = 1.041366624 Solving -0.5333333335 + x = 1.041366624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + x = 1.041366624 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + x = 1.041366624 + 0.5333333335 x = 1.041366624 + 0.5333333335 Combine like terms: 1.041366624 + 0.5333333335 = 1.5746999575 x = 1.5746999575 Simplifying x = 1.5746999575Subproblem 2
x + -0.5333333335 = -1.041366624 Simplifying x + -0.5333333335 = -1.041366624 Reorder the terms: -0.5333333335 + x = -1.041366624 Solving -0.5333333335 + x = -1.041366624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5333333335' to each side of the equation. -0.5333333335 + 0.5333333335 + x = -1.041366624 + 0.5333333335 Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000 0.0000000000 + x = -1.041366624 + 0.5333333335 x = -1.041366624 + 0.5333333335 Combine like terms: -1.041366624 + 0.5333333335 = -0.5080332905 x = -0.5080332905 Simplifying x = -0.5080332905Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5746999575, -0.5080332905}
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