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Simplifying x4 + -27x2 + 63 = 0 Reorder the terms: 63 + -27x2 + x4 = 0 Solving 63 + -27x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + -27x2 + -63 + x4 = 0 + -63 Reorder the terms: 63 + -63 + -27x2 + x4 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -27x2 + x4 = 0 + -63 -27x2 + x4 = 0 + -63 Combine like terms: 0 + -63 = -63 -27x2 + x4 = -63 The x term is -27x2. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x2 + 182.25 + x4 = -63 + 182.25 Reorder the terms: 182.25 + -27x2 + x4 = -63 + 182.25 Combine like terms: -63 + 182.25 = 119.25 182.25 + -27x2 + x4 = 119.25 Factor a perfect square on the left side: (x2 + -13.5)(x2 + -13.5) = 119.25 Calculate the square root of the right side: 10.920164834 Break this problem into two subproblems by setting (x2 + -13.5) equal to 10.920164834 and -10.920164834.Subproblem 1
x2 + -13.5 = 10.920164834 Simplifying x2 + -13.5 = 10.920164834 Reorder the terms: -13.5 + x2 = 10.920164834 Solving -13.5 + x2 = 10.920164834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x2 = 10.920164834 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x2 = 10.920164834 + 13.5 x2 = 10.920164834 + 13.5 Combine like terms: 10.920164834 + 13.5 = 24.420164834 x2 = 24.420164834 Simplifying x2 = 24.420164834 Take the square root of each side: x = {-4.941676318, 4.941676318}Subproblem 2
x2 + -13.5 = -10.920164834 Simplifying x2 + -13.5 = -10.920164834 Reorder the terms: -13.5 + x2 = -10.920164834 Solving -13.5 + x2 = -10.920164834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x2 = -10.920164834 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x2 = -10.920164834 + 13.5 x2 = -10.920164834 + 13.5 Combine like terms: -10.920164834 + 13.5 = 2.579835166 x2 = 2.579835166 Simplifying x2 = 2.579835166 Take the square root of each side: x = {-1.606186529, 1.606186529}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.941676318, 4.941676318, -1.606186529, 1.606186529}
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