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Simplifying 64x4 + -720x2 = -81 Reorder the terms: -720x2 + 64x4 = -81 Solving -720x2 + 64x4 = -81 Solving for variable 'x'. Reorder the terms: 81 + -720x2 + 64x4 = -81 + 81 Combine like terms: -81 + 81 = 0 81 + -720x2 + 64x4 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 1.265625 + -11.25x2 + x4 = 0 Move the constant term to the right: Add '-1.265625' to each side of the equation. 1.265625 + -11.25x2 + -1.265625 + x4 = 0 + -1.265625 Reorder the terms: 1.265625 + -1.265625 + -11.25x2 + x4 = 0 + -1.265625 Combine like terms: 1.265625 + -1.265625 = 0.000000 0.000000 + -11.25x2 + x4 = 0 + -1.265625 -11.25x2 + x4 = 0 + -1.265625 Combine like terms: 0 + -1.265625 = -1.265625 -11.25x2 + x4 = -1.265625 The x term is -11.25x2. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x2 + 31.640625 + x4 = -1.265625 + 31.640625 Reorder the terms: 31.640625 + -11.25x2 + x4 = -1.265625 + 31.640625 Combine like terms: -1.265625 + 31.640625 = 30.375 31.640625 + -11.25x2 + x4 = 30.375 Factor a perfect square on the left side: (x2 + -5.625)(x2 + -5.625) = 30.375 Calculate the square root of the right side: 5.511351921 Break this problem into two subproblems by setting (x2 + -5.625) equal to 5.511351921 and -5.511351921.Subproblem 1
x2 + -5.625 = 5.511351921 Simplifying x2 + -5.625 = 5.511351921 Reorder the terms: -5.625 + x2 = 5.511351921 Solving -5.625 + x2 = 5.511351921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x2 = 5.511351921 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x2 = 5.511351921 + 5.625 x2 = 5.511351921 + 5.625 Combine like terms: 5.511351921 + 5.625 = 11.136351921 x2 = 11.136351921 Simplifying x2 = 11.136351921 Take the square root of each side: x = {-3.337117307, 3.337117307}Subproblem 2
x2 + -5.625 = -5.511351921 Simplifying x2 + -5.625 = -5.511351921 Reorder the terms: -5.625 + x2 = -5.511351921 Solving -5.625 + x2 = -5.511351921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x2 = -5.511351921 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x2 = -5.511351921 + 5.625 x2 = -5.511351921 + 5.625 Combine like terms: -5.511351921 + 5.625 = 0.113648079 x2 = 0.113648079 Simplifying x2 = 0.113648079 Take the square root of each side: x = {-0.337117307, 0.337117307}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.337117307, 3.337117307, -0.337117307, 0.337117307}
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