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Simplifying 7x4 + 6x2 + -27 = 0 Reorder the terms: -27 + 6x2 + 7x4 = 0 Solving -27 + 6x2 + 7x4 = 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'. -3.857142857 + 0.8571428571x2 + x4 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + 0.8571428571x2 + 3.857142857 + x4 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + 0.8571428571x2 + x4 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + 0.8571428571x2 + x4 = 0 + 3.857142857 0.8571428571x2 + x4 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 0.8571428571x2 + x4 = 3.857142857 The x term is 0.8571428571x2. 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. 0.8571428571x2 + 0.1836734694 + x4 = 3.857142857 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x2 + x4 = 3.857142857 + 0.1836734694 Combine like terms: 3.857142857 + 0.1836734694 = 4.0408163264 0.1836734694 + 0.8571428571x2 + x4 = 4.0408163264 Factor a perfect square on the left side: (x2 + 0.4285714286)(x2 + 0.4285714286) = 4.0408163264 Calculate the square root of the right side: 2.010178183 Break this problem into two subproblems by setting (x2 + 0.4285714286) equal to 2.010178183 and -2.010178183.Subproblem 1
x2 + 0.4285714286 = 2.010178183 Simplifying x2 + 0.4285714286 = 2.010178183 Reorder the terms: 0.4285714286 + x2 = 2.010178183 Solving 0.4285714286 + x2 = 2.010178183 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 + x2 = 2.010178183 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x2 = 2.010178183 + -0.4285714286 x2 = 2.010178183 + -0.4285714286 Combine like terms: 2.010178183 + -0.4285714286 = 1.5816067544 x2 = 1.5816067544 Simplifying x2 = 1.5816067544 Take the square root of each side: x = {-1.257619479, 1.257619479}Subproblem 2
x2 + 0.4285714286 = -2.010178183 Simplifying x2 + 0.4285714286 = -2.010178183 Reorder the terms: 0.4285714286 + x2 = -2.010178183 Solving 0.4285714286 + x2 = -2.010178183 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 + x2 = -2.010178183 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x2 = -2.010178183 + -0.4285714286 x2 = -2.010178183 + -0.4285714286 Combine like terms: -2.010178183 + -0.4285714286 = -2.4387496116 x2 = -2.4387496116 Simplifying x2 = -2.4387496116 Reorder the terms: 2.4387496116 + x2 = -2.4387496116 + 2.4387496116 Combine like terms: -2.4387496116 + 2.4387496116 = 0.0000000000 2.4387496116 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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