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Simplifying x4 + -12x2 + 30 = 0 Reorder the terms: 30 + -12x2 + x4 = 0 Solving 30 + -12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12x2 + -30 + x4 = 0 + -30 Reorder the terms: 30 + -30 + -12x2 + x4 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12x2 + x4 = 0 + -30 -12x2 + x4 = 0 + -30 Combine like terms: 0 + -30 = -30 -12x2 + x4 = -30 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = -30 + 36 Reorder the terms: 36 + -12x2 + x4 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + -12x2 + x4 = 6 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + -6) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + -6 = 2.449489743 Simplifying x2 + -6 = 2.449489743 Reorder the terms: -6 + x2 = 2.449489743 Solving -6 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 2.449489743 + 6 x2 = 2.449489743 + 6 Combine like terms: 2.449489743 + 6 = 8.449489743 x2 = 8.449489743 Simplifying x2 = 8.449489743 Take the square root of each side: x = {-2.906800603, 2.906800603}Subproblem 2
x2 + -6 = -2.449489743 Simplifying x2 + -6 = -2.449489743 Reorder the terms: -6 + x2 = -2.449489743 Solving -6 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -2.449489743 + 6 x2 = -2.449489743 + 6 Combine like terms: -2.449489743 + 6 = 3.550510257 x2 = 3.550510257 Simplifying x2 = 3.550510257 Take the square root of each side: x = {-1.884279771, 1.884279771}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.906800603, 2.906800603, -1.884279771, 1.884279771}
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