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Simplifying 4x4 + -36x2 + 9 = 0 Reorder the terms: 9 + -36x2 + 4x4 = 0 Solving 9 + -36x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -9x2 + x4 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -9x2 + -2.25 + x4 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -9x2 + x4 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -9x2 + x4 = 0 + -2.25 -9x2 + x4 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -9x2 + x4 = -2.25 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = -2.25 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = -2.25 + 20.25 Combine like terms: -2.25 + 20.25 = 18 20.25 + -9x2 + x4 = 18 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x2 + -4.5) equal to 4.242640687 and -4.242640687.Subproblem 1
x2 + -4.5 = 4.242640687 Simplifying x2 + -4.5 = 4.242640687 Reorder the terms: -4.5 + x2 = 4.242640687 Solving -4.5 + x2 = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 4.242640687 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 4.242640687 + 4.5 x2 = 4.242640687 + 4.5 Combine like terms: 4.242640687 + 4.5 = 8.742640687 x2 = 8.742640687 Simplifying x2 = 8.742640687 Take the square root of each side: x = {-2.956795679, 2.956795679}Subproblem 2
x2 + -4.5 = -4.242640687 Simplifying x2 + -4.5 = -4.242640687 Reorder the terms: -4.5 + x2 = -4.242640687 Solving -4.5 + x2 = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -4.242640687 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -4.242640687 + 4.5 x2 = -4.242640687 + 4.5 Combine like terms: -4.242640687 + 4.5 = 0.257359313 x2 = 0.257359313 Simplifying x2 = 0.257359313 Take the square root of each side: x = {-0.507305936, 0.507305936}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.956795679, 2.956795679, -0.507305936, 0.507305936}
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