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Simplifying 9x4 + -72x2 + 64 = 0 Reorder the terms: 64 + -72x2 + 9x4 = 0 Solving 64 + -72x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 7.111111111 + -8x2 + x4 = 0 Move the constant term to the right: Add '-7.111111111' to each side of the equation. 7.111111111 + -8x2 + -7.111111111 + x4 = 0 + -7.111111111 Reorder the terms: 7.111111111 + -7.111111111 + -8x2 + x4 = 0 + -7.111111111 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 0.000000000 + -8x2 + x4 = 0 + -7.111111111 -8x2 + x4 = 0 + -7.111111111 Combine like terms: 0 + -7.111111111 = -7.111111111 -8x2 + x4 = -7.111111111 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -7.111111111 + 16 Reorder the terms: 16 + -8x2 + x4 = -7.111111111 + 16 Combine like terms: -7.111111111 + 16 = 8.888888889 16 + -8x2 + x4 = 8.888888889 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 8.888888889 Calculate the square root of the right side: 2.98142397 Break this problem into two subproblems by setting (x2 + -4) equal to 2.98142397 and -2.98142397.Subproblem 1
x2 + -4 = 2.98142397 Simplifying x2 + -4 = 2.98142397 Reorder the terms: -4 + x2 = 2.98142397 Solving -4 + x2 = 2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 2.98142397 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 2.98142397 + 4 x2 = 2.98142397 + 4 Combine like terms: 2.98142397 + 4 = 6.98142397 x2 = 6.98142397 Simplifying x2 = 6.98142397 Take the square root of each side: x = {-2.642238439, 2.642238439}Subproblem 2
x2 + -4 = -2.98142397 Simplifying x2 + -4 = -2.98142397 Reorder the terms: -4 + x2 = -2.98142397 Solving -4 + x2 = -2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -2.98142397 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -2.98142397 + 4 x2 = -2.98142397 + 4 Combine like terms: -2.98142397 + 4 = 1.01857603 x2 = 1.01857603 Simplifying x2 = 1.01857603 Take the square root of each side: x = {-1.009245277, 1.009245277}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.642238439, 2.642238439, -1.009245277, 1.009245277}
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