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Simplifying 20x4 + 49x2 + -9 = 0 Reorder the terms: -9 + 49x2 + 20x4 = 0 Solving -9 + 49x2 + 20x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + 2.45x2 + x4 = 0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 2.45x2 + 0.45 + x4 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 2.45x2 + x4 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 2.45x2 + x4 = 0 + 0.45 2.45x2 + x4 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 2.45x2 + x4 = 0.45 The x term is 2.45x2. Take half its coefficient (1.225). Square it (1.500625) and add it to both sides. Add '1.500625' to each side of the equation. 2.45x2 + 1.500625 + x4 = 0.45 + 1.500625 Reorder the terms: 1.500625 + 2.45x2 + x4 = 0.45 + 1.500625 Combine like terms: 0.45 + 1.500625 = 1.950625 1.500625 + 2.45x2 + x4 = 1.950625 Factor a perfect square on the left side: (x2 + 1.225)(x2 + 1.225) = 1.950625 Calculate the square root of the right side: 1.396647772 Break this problem into two subproblems by setting (x2 + 1.225) equal to 1.396647772 and -1.396647772.Subproblem 1
x2 + 1.225 = 1.396647772 Simplifying x2 + 1.225 = 1.396647772 Reorder the terms: 1.225 + x2 = 1.396647772 Solving 1.225 + x2 = 1.396647772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.225' to each side of the equation. 1.225 + -1.225 + x2 = 1.396647772 + -1.225 Combine like terms: 1.225 + -1.225 = 0.000 0.000 + x2 = 1.396647772 + -1.225 x2 = 1.396647772 + -1.225 Combine like terms: 1.396647772 + -1.225 = 0.171647772 x2 = 0.171647772 Simplifying x2 = 0.171647772 Take the square root of each side: x = {-0.414303961, 0.414303961}Subproblem 2
x2 + 1.225 = -1.396647772 Simplifying x2 + 1.225 = -1.396647772 Reorder the terms: 1.225 + x2 = -1.396647772 Solving 1.225 + x2 = -1.396647772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.225' to each side of the equation. 1.225 + -1.225 + x2 = -1.396647772 + -1.225 Combine like terms: 1.225 + -1.225 = 0.000 0.000 + x2 = -1.396647772 + -1.225 x2 = -1.396647772 + -1.225 Combine like terms: -1.396647772 + -1.225 = -2.621647772 x2 = -2.621647772 Simplifying x2 = -2.621647772 Reorder the terms: 2.621647772 + x2 = -2.621647772 + 2.621647772 Combine like terms: -2.621647772 + 2.621647772 = 0.000000000 2.621647772 + x2 = 0.000000000 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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