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Simplifying (x2 + -8x + -6) + -1(-8x2 + 4x + 1) = 0 Reorder the terms: (-6 + -8x + x2) + -1(-8x2 + 4x + 1) = 0 Remove parenthesis around (-6 + -8x + x2) -6 + -8x + x2 + -1(-8x2 + 4x + 1) = 0 Reorder the terms: -6 + -8x + x2 + -1(1 + 4x + -8x2) = 0 -6 + -8x + x2 + (1 * -1 + 4x * -1 + -8x2 * -1) = 0 -6 + -8x + x2 + (-1 + -4x + 8x2) = 0 Reorder the terms: -6 + -1 + -8x + -4x + x2 + 8x2 = 0 Combine like terms: -6 + -1 = -7 -7 + -8x + -4x + x2 + 8x2 = 0 Combine like terms: -8x + -4x = -12x -7 + -12x + x2 + 8x2 = 0 Combine like terms: x2 + 8x2 = 9x2 -7 + -12x + 9x2 = 0 Solving -7 + -12x + 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'. -0.7777777778 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -1.333333333x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -1.333333333x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + 0.7777777778 -1.333333333x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -1.333333333x + x2 = 0.7777777778 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 0.7777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.7777777778 + 0.4444444442 Combine like terms: 0.7777777778 + 0.4444444442 = 1.222222222 0.4444444442 + -1.333333333x + x2 = 1.222222222 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 1.222222222 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.105541597 and -1.105541597.Subproblem 1
x + -0.6666666665 = 1.105541597 Simplifying x + -0.6666666665 = 1.105541597 Reorder the terms: -0.6666666665 + x = 1.105541597 Solving -0.6666666665 + x = 1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.105541597 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.105541597 + 0.6666666665 x = 1.105541597 + 0.6666666665 Combine like terms: 1.105541597 + 0.6666666665 = 1.7722082635 x = 1.7722082635 Simplifying x = 1.7722082635Subproblem 2
x + -0.6666666665 = -1.105541597 Simplifying x + -0.6666666665 = -1.105541597 Reorder the terms: -0.6666666665 + x = -1.105541597 Solving -0.6666666665 + x = -1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.105541597 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.105541597 + 0.6666666665 x = -1.105541597 + 0.6666666665 Combine like terms: -1.105541597 + 0.6666666665 = -0.4388749305 x = -0.4388749305 Simplifying x = -0.4388749305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7722082635, -0.4388749305}
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