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Simplifying 35x4 + -30x2 + 3 = 0 Reorder the terms: 3 + -30x2 + 35x4 = 0 Solving 3 + -30x2 + 35x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.08571428571 + -0.8571428571x2 + x4 = 0 Move the constant term to the right: Add '-0.08571428571' to each side of the equation. 0.08571428571 + -0.8571428571x2 + -0.08571428571 + x4 = 0 + -0.08571428571 Reorder the terms: 0.08571428571 + -0.08571428571 + -0.8571428571x2 + x4 = 0 + -0.08571428571 Combine like terms: 0.08571428571 + -0.08571428571 = 0.00000000000 0.00000000000 + -0.8571428571x2 + x4 = 0 + -0.08571428571 -0.8571428571x2 + x4 = 0 + -0.08571428571 Combine like terms: 0 + -0.08571428571 = -0.08571428571 -0.8571428571x2 + x4 = -0.08571428571 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 = -0.08571428571 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x2 + x4 = -0.08571428571 + 0.1836734694 Combine like terms: -0.08571428571 + 0.1836734694 = 0.09795918369 0.1836734694 + -0.8571428571x2 + x4 = 0.09795918369 Factor a perfect square on the left side: (x2 + -0.4285714286)(x2 + -0.4285714286) = 0.09795918369 Calculate the square root of the right side: 0.312984319 Break this problem into two subproblems by setting (x2 + -0.4285714286) equal to 0.312984319 and -0.312984319.Subproblem 1
x2 + -0.4285714286 = 0.312984319 Simplifying x2 + -0.4285714286 = 0.312984319 Reorder the terms: -0.4285714286 + x2 = 0.312984319 Solving -0.4285714286 + x2 = 0.312984319 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 = 0.312984319 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x2 = 0.312984319 + 0.4285714286 x2 = 0.312984319 + 0.4285714286 Combine like terms: 0.312984319 + 0.4285714286 = 0.7415557476 x2 = 0.7415557476 Simplifying x2 = 0.7415557476 Take the square root of each side: x = {-0.861136312, 0.861136312}Subproblem 2
x2 + -0.4285714286 = -0.312984319 Simplifying x2 + -0.4285714286 = -0.312984319 Reorder the terms: -0.4285714286 + x2 = -0.312984319 Solving -0.4285714286 + x2 = -0.312984319 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 = -0.312984319 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x2 = -0.312984319 + 0.4285714286 x2 = -0.312984319 + 0.4285714286 Combine like terms: -0.312984319 + 0.4285714286 = 0.1155871096 x2 = 0.1155871096 Simplifying x2 = 0.1155871096 Take the square root of each side: x = {-0.339981043, 0.339981043}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.861136312, 0.861136312, -0.339981043, 0.339981043}
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