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Simplifying x4 + -18x2 + 36 = 0 Reorder the terms: 36 + -18x2 + x4 = 0 Solving 36 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -18x2 + -36 + x4 = 0 + -36 Reorder the terms: 36 + -36 + -18x2 + x4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -18x2 + x4 = 0 + -36 -18x2 + x4 = 0 + -36 Combine like terms: 0 + -36 = -36 -18x2 + x4 = -36 The x term is -18x2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x2 + 81 + x4 = -36 + 81 Reorder the terms: 81 + -18x2 + x4 = -36 + 81 Combine like terms: -36 + 81 = 45 81 + -18x2 + x4 = 45 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x2 + -9) equal to 6.708203933 and -6.708203933.Subproblem 1
x2 + -9 = 6.708203933 Simplifying x2 + -9 = 6.708203933 Reorder the terms: -9 + x2 = 6.708203933 Solving -9 + x2 = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 6.708203933 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 6.708203933 + 9 x2 = 6.708203933 + 9 Combine like terms: 6.708203933 + 9 = 15.708203933 x2 = 15.708203933 Simplifying x2 = 15.708203933 Take the square root of each side: x = {-3.963357659, 3.963357659}Subproblem 2
x2 + -9 = -6.708203933 Simplifying x2 + -9 = -6.708203933 Reorder the terms: -9 + x2 = -6.708203933 Solving -9 + x2 = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = -6.708203933 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -6.708203933 + 9 x2 = -6.708203933 + 9 Combine like terms: -6.708203933 + 9 = 2.291796067 x2 = 2.291796067 Simplifying x2 = 2.291796067 Take the square root of each side: x = {-1.513867916, 1.513867916}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.963357659, 3.963357659, -1.513867916, 1.513867916}
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