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Simplifying (-6x2 + 5x + -2) + -1(7x2 + -5x + -8) = 0 Reorder the terms: (-2 + 5x + -6x2) + -1(7x2 + -5x + -8) = 0 Remove parenthesis around (-2 + 5x + -6x2) -2 + 5x + -6x2 + -1(7x2 + -5x + -8) = 0 Reorder the terms: -2 + 5x + -6x2 + -1(-8 + -5x + 7x2) = 0 -2 + 5x + -6x2 + (-8 * -1 + -5x * -1 + 7x2 * -1) = 0 -2 + 5x + -6x2 + (8 + 5x + -7x2) = 0 Reorder the terms: -2 + 8 + 5x + 5x + -6x2 + -7x2 = 0 Combine like terms: -2 + 8 = 6 6 + 5x + 5x + -6x2 + -7x2 = 0 Combine like terms: 5x + 5x = 10x 6 + 10x + -6x2 + -7x2 = 0 Combine like terms: -6x2 + -7x2 = -13x2 6 + 10x + -13x2 = 0 Solving 6 + 10x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.4615384615 + -0.7692307692x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + -0.7692307692x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + -0.7692307692x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + -0.7692307692x + x2 = 0 + 0.4615384615 -0.7692307692x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 -0.7692307692x + x2 = 0.4615384615 The x term is -0.7692307692x. Take half its coefficient (-0.3846153846). Square it (0.1479289941) and add it to both sides. Add '0.1479289941' to each side of the equation. -0.7692307692x + 0.1479289941 + x2 = 0.4615384615 + 0.1479289941 Reorder the terms: 0.1479289941 + -0.7692307692x + x2 = 0.4615384615 + 0.1479289941 Combine like terms: 0.4615384615 + 0.1479289941 = 0.6094674556 0.1479289941 + -0.7692307692x + x2 = 0.6094674556 Factor a perfect square on the left side: (x + -0.3846153846)(x + -0.3846153846) = 0.6094674556 Calculate the square root of the right side: 0.780683967 Break this problem into two subproblems by setting (x + -0.3846153846) equal to 0.780683967 and -0.780683967.Subproblem 1
x + -0.3846153846 = 0.780683967 Simplifying x + -0.3846153846 = 0.780683967 Reorder the terms: -0.3846153846 + x = 0.780683967 Solving -0.3846153846 + x = 0.780683967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846 + x = 0.780683967 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + x = 0.780683967 + 0.3846153846 x = 0.780683967 + 0.3846153846 Combine like terms: 0.780683967 + 0.3846153846 = 1.1652993516 x = 1.1652993516 Simplifying x = 1.1652993516Subproblem 2
x + -0.3846153846 = -0.780683967 Simplifying x + -0.3846153846 = -0.780683967 Reorder the terms: -0.3846153846 + x = -0.780683967 Solving -0.3846153846 + x = -0.780683967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846 + x = -0.780683967 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + x = -0.780683967 + 0.3846153846 x = -0.780683967 + 0.3846153846 Combine like terms: -0.780683967 + 0.3846153846 = -0.3960685824 x = -0.3960685824 Simplifying x = -0.3960685824Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1652993516, -0.3960685824}
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