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Simplifying 72x4 + -32x2 + 1 = 0 Reorder the terms: 1 + -32x2 + 72x4 = 0 Solving 1 + -32x2 + 72x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 0.01388888889 + -0.4444444444x2 + x4 = 0 Move the constant term to the right: Add '-0.01388888889' to each side of the equation. 0.01388888889 + -0.4444444444x2 + -0.01388888889 + x4 = 0 + -0.01388888889 Reorder the terms: 0.01388888889 + -0.01388888889 + -0.4444444444x2 + x4 = 0 + -0.01388888889 Combine like terms: 0.01388888889 + -0.01388888889 = 0.00000000000 0.00000000000 + -0.4444444444x2 + x4 = 0 + -0.01388888889 -0.4444444444x2 + x4 = 0 + -0.01388888889 Combine like terms: 0 + -0.01388888889 = -0.01388888889 -0.4444444444x2 + x4 = -0.01388888889 The x term is -0.4444444444x2. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x2 + 0.04938271604 + x4 = -0.01388888889 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x2 + x4 = -0.01388888889 + 0.04938271604 Combine like terms: -0.01388888889 + 0.04938271604 = 0.03549382715 0.04938271604 + -0.4444444444x2 + x4 = 0.03549382715 Factor a perfect square on the left side: (x2 + -0.2222222222)(x2 + -0.2222222222) = 0.03549382715 Calculate the square root of the right side: 0.188398055 Break this problem into two subproblems by setting (x2 + -0.2222222222) equal to 0.188398055 and -0.188398055.Subproblem 1
x2 + -0.2222222222 = 0.188398055 Simplifying x2 + -0.2222222222 = 0.188398055 Reorder the terms: -0.2222222222 + x2 = 0.188398055 Solving -0.2222222222 + x2 = 0.188398055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x2 = 0.188398055 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x2 = 0.188398055 + 0.2222222222 x2 = 0.188398055 + 0.2222222222 Combine like terms: 0.188398055 + 0.2222222222 = 0.4106202772 x2 = 0.4106202772 Simplifying x2 = 0.4106202772 Take the square root of each side: x = {-0.640796596, 0.640796596}Subproblem 2
x2 + -0.2222222222 = -0.188398055 Simplifying x2 + -0.2222222222 = -0.188398055 Reorder the terms: -0.2222222222 + x2 = -0.188398055 Solving -0.2222222222 + x2 = -0.188398055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x2 = -0.188398055 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x2 = -0.188398055 + 0.2222222222 x2 = -0.188398055 + 0.2222222222 Combine like terms: -0.188398055 + 0.2222222222 = 0.0338241672 x2 = 0.0338241672 Simplifying x2 = 0.0338241672 Take the square root of each side: x = {-0.183913477, 0.183913477}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.640796596, 0.640796596, -0.183913477, 0.183913477}
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