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Simplifying 7x2 + -6x + -3 = 0 Reorder the terms: -3 + -6x + 7x2 = 0 Solving -3 + -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'. -0.4285714286 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.8571428571x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.8571428571x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.4285714286 -0.8571428571x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.8571428571x + x2 = 0.4285714286 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 = 0.4285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.4285714286 + 0.1836734694 Combine like terms: 0.4285714286 + 0.1836734694 = 0.612244898 0.1836734694 + -0.8571428571x + x2 = 0.612244898 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.612244898 Calculate the square root of the right side: 0.782460796 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.782460796 and -0.782460796.Subproblem 1
x + -0.4285714286 = 0.782460796 Simplifying x + -0.4285714286 = 0.782460796 Reorder the terms: -0.4285714286 + x = 0.782460796 Solving -0.4285714286 + x = 0.782460796 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 = 0.782460796 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.782460796 + 0.4285714286 x = 0.782460796 + 0.4285714286 Combine like terms: 0.782460796 + 0.4285714286 = 1.2110322246 x = 1.2110322246 Simplifying x = 1.2110322246Subproblem 2
x + -0.4285714286 = -0.782460796 Simplifying x + -0.4285714286 = -0.782460796 Reorder the terms: -0.4285714286 + x = -0.782460796 Solving -0.4285714286 + x = -0.782460796 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 = -0.782460796 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.782460796 + 0.4285714286 x = -0.782460796 + 0.4285714286 Combine like terms: -0.782460796 + 0.4285714286 = -0.3538893674 x = -0.3538893674 Simplifying x = -0.3538893674Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2110322246, -0.3538893674}
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