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Simplifying 7x2 + -6x + -32 = 0 Reorder the terms: -32 + -6x + 7x2 = 0 Solving -32 + -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'. -4.571428571 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + -0.8571428571x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + -0.8571428571x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 4.571428571 -0.8571428571x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 -0.8571428571x + x2 = 4.571428571 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 = 4.571428571 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 4.571428571 + 0.1836734694 Combine like terms: 4.571428571 + 0.1836734694 = 4.7551020404 0.1836734694 + -0.8571428571x + x2 = 4.7551020404 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 4.7551020404 Calculate the square root of the right side: 2.180619646 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 2.180619646 and -2.180619646.Subproblem 1
x + -0.4285714286 = 2.180619646 Simplifying x + -0.4285714286 = 2.180619646 Reorder the terms: -0.4285714286 + x = 2.180619646 Solving -0.4285714286 + x = 2.180619646 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 = 2.180619646 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 2.180619646 + 0.4285714286 x = 2.180619646 + 0.4285714286 Combine like terms: 2.180619646 + 0.4285714286 = 2.6091910746 x = 2.6091910746 Simplifying x = 2.6091910746Subproblem 2
x + -0.4285714286 = -2.180619646 Simplifying x + -0.4285714286 = -2.180619646 Reorder the terms: -0.4285714286 + x = -2.180619646 Solving -0.4285714286 + x = -2.180619646 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 = -2.180619646 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -2.180619646 + 0.4285714286 x = -2.180619646 + 0.4285714286 Combine like terms: -2.180619646 + 0.4285714286 = -1.7520482174 x = -1.7520482174 Simplifying x = -1.7520482174Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6091910746, -1.7520482174}
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