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Simplifying 2x2 + -4x + 8x2 + -3(x + 2) + -1x2 + -2 = 0 Reorder the terms: 2x2 + -4x + 8x2 + -3(2 + x) + -1x2 + -2 = 0 2x2 + -4x + 8x2 + (2 * -3 + x * -3) + -1x2 + -2 = 0 2x2 + -4x + 8x2 + (-6 + -3x) + -1x2 + -2 = 0 Reorder the terms: -6 + -2 + -4x + -3x + 2x2 + 8x2 + -1x2 = 0 Combine like terms: -6 + -2 = -8 -8 + -4x + -3x + 2x2 + 8x2 + -1x2 = 0 Combine like terms: -4x + -3x = -7x -8 + -7x + 2x2 + 8x2 + -1x2 = 0 Combine like terms: 2x2 + 8x2 = 10x2 -8 + -7x + 10x2 + -1x2 = 0 Combine like terms: 10x2 + -1x2 = 9x2 -8 + -7x + 9x2 = 0 Solving -8 + -7x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.7777777778x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.7777777778x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.7777777778x + x2 = 0 + 0.8888888889 -0.7777777778x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.7777777778x + x2 = 0.8888888889 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = 0.8888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 0.8888888889 + 0.1512345679 Combine like terms: 0.8888888889 + 0.1512345679 = 1.0401234568 0.1512345679 + -0.7777777778x + x2 = 1.0401234568 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 1.0401234568 Calculate the square root of the right side: 1.019864431 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 1.019864431 and -1.019864431.Subproblem 1
x + -0.3888888889 = 1.019864431 Simplifying x + -0.3888888889 = 1.019864431 Reorder the terms: -0.3888888889 + x = 1.019864431 Solving -0.3888888889 + x = 1.019864431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 1.019864431 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 1.019864431 + 0.3888888889 x = 1.019864431 + 0.3888888889 Combine like terms: 1.019864431 + 0.3888888889 = 1.4087533199 x = 1.4087533199 Simplifying x = 1.4087533199Subproblem 2
x + -0.3888888889 = -1.019864431 Simplifying x + -0.3888888889 = -1.019864431 Reorder the terms: -0.3888888889 + x = -1.019864431 Solving -0.3888888889 + x = -1.019864431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -1.019864431 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -1.019864431 + 0.3888888889 x = -1.019864431 + 0.3888888889 Combine like terms: -1.019864431 + 0.3888888889 = -0.6309755421 x = -0.6309755421 Simplifying x = -0.6309755421Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4087533199, -0.6309755421}
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