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Simplifying (6x2 + 8x + -5) + (x2 + -2x + -6) = 0 Reorder the terms: (-5 + 8x + 6x2) + (x2 + -2x + -6) = 0 Remove parenthesis around (-5 + 8x + 6x2) -5 + 8x + 6x2 + (x2 + -2x + -6) = 0 Reorder the terms: -5 + 8x + 6x2 + (-6 + -2x + x2) = 0 Remove parenthesis around (-6 + -2x + x2) -5 + 8x + 6x2 + -6 + -2x + x2 = 0 Reorder the terms: -5 + -6 + 8x + -2x + 6x2 + x2 = 0 Combine like terms: -5 + -6 = -11 -11 + 8x + -2x + 6x2 + x2 = 0 Combine like terms: 8x + -2x = 6x -11 + 6x + 6x2 + x2 = 0 Combine like terms: 6x2 + x2 = 7x2 -11 + 6x + 7x2 = 0 Solving -11 + 6x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + 0.8571428571x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + 0.8571428571x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + 1.571428571 0.8571428571x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 0.8571428571x + x2 = 1.571428571 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = 1.571428571 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 1.571428571 + 0.1836734694 Combine like terms: 1.571428571 + 0.1836734694 = 1.7551020404 0.1836734694 + 0.8571428571x + x2 = 1.7551020404 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 1.7551020404 Calculate the square root of the right side: 1.324802642 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 1.324802642 and -1.324802642.Subproblem 1
x + 0.4285714286 = 1.324802642 Simplifying x + 0.4285714286 = 1.324802642 Reorder the terms: 0.4285714286 + x = 1.324802642 Solving 0.4285714286 + x = 1.324802642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 1.324802642 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.324802642 + -0.4285714286 x = 1.324802642 + -0.4285714286 Combine like terms: 1.324802642 + -0.4285714286 = 0.8962312134 x = 0.8962312134 Simplifying x = 0.8962312134Subproblem 2
x + 0.4285714286 = -1.324802642 Simplifying x + 0.4285714286 = -1.324802642 Reorder the terms: 0.4285714286 + x = -1.324802642 Solving 0.4285714286 + x = -1.324802642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -1.324802642 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.324802642 + -0.4285714286 x = -1.324802642 + -0.4285714286 Combine like terms: -1.324802642 + -0.4285714286 = -1.7533740706 x = -1.7533740706 Simplifying x = -1.7533740706Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8962312134, -1.7533740706}
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