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Simplifying 343x4 + -294x2 + 60 = 0 Reorder the terms: 60 + -294x2 + 343x4 = 0 Solving 60 + -294x2 + 343x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 343 the coefficient of the squared term: Divide each side by '343'. 0.1749271137 + -0.8571428571x2 + x4 = 0 Move the constant term to the right: Add '-0.1749271137' to each side of the equation. 0.1749271137 + -0.8571428571x2 + -0.1749271137 + x4 = 0 + -0.1749271137 Reorder the terms: 0.1749271137 + -0.1749271137 + -0.8571428571x2 + x4 = 0 + -0.1749271137 Combine like terms: 0.1749271137 + -0.1749271137 = 0.0000000000 0.0000000000 + -0.8571428571x2 + x4 = 0 + -0.1749271137 -0.8571428571x2 + x4 = 0 + -0.1749271137 Combine like terms: 0 + -0.1749271137 = -0.1749271137 -0.8571428571x2 + x4 = -0.1749271137 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 = -0.1749271137 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x2 + x4 = -0.1749271137 + 0.1836734694 Combine like terms: -0.1749271137 + 0.1836734694 = 0.0087463557 0.1836734694 + -0.8571428571x2 + x4 = 0.0087463557 Factor a perfect square on the left side: (x2 + -0.4285714286)(x2 + -0.4285714286) = 0.0087463557 Calculate the square root of the right side: 0.093521953 Break this problem into two subproblems by setting (x2 + -0.4285714286) equal to 0.093521953 and -0.093521953.Subproblem 1
x2 + -0.4285714286 = 0.093521953 Simplifying x2 + -0.4285714286 = 0.093521953 Reorder the terms: -0.4285714286 + x2 = 0.093521953 Solving -0.4285714286 + x2 = 0.093521953 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 = 0.093521953 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x2 = 0.093521953 + 0.4285714286 x2 = 0.093521953 + 0.4285714286 Combine like terms: 0.093521953 + 0.4285714286 = 0.5220933816 x2 = 0.5220933816 Simplifying x2 = 0.5220933816 Take the square root of each side: x = {-0.722560296, 0.722560296}Subproblem 2
x2 + -0.4285714286 = -0.093521953 Simplifying x2 + -0.4285714286 = -0.093521953 Reorder the terms: -0.4285714286 + x2 = -0.093521953 Solving -0.4285714286 + x2 = -0.093521953 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 = -0.093521953 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x2 = -0.093521953 + 0.4285714286 x2 = -0.093521953 + 0.4285714286 Combine like terms: -0.093521953 + 0.4285714286 = 0.3350494756 x2 = 0.3350494756 Simplifying x2 = 0.3350494756 Take the square root of each side: x = {-0.578834584, 0.578834584}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.722560296, 0.722560296, -0.578834584, 0.578834584}
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