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Simplifying -9x4 + 36x2 + -16 = 0 Reorder the terms: -16 + 36x2 + -9x4 = 0 Solving -16 + 36x2 + -9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 1.777777778 + -4x2 + x4 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + -4x2 + -1.777777778 + x4 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + -4x2 + x4 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + -4x2 + x4 = 0 + -1.777777778 -4x2 + x4 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 -4x2 + x4 = -1.777777778 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = -1.777777778 + 4 Reorder the terms: 4 + -4x2 + x4 = -1.777777778 + 4 Combine like terms: -1.777777778 + 4 = 2.222222222 4 + -4x2 + x4 = 2.222222222 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 2.222222222 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (x2 + -2) equal to 1.490711985 and -1.490711985.Subproblem 1
x2 + -2 = 1.490711985 Simplifying x2 + -2 = 1.490711985 Reorder the terms: -2 + x2 = 1.490711985 Solving -2 + x2 = 1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 1.490711985 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 1.490711985 + 2 x2 = 1.490711985 + 2 Combine like terms: 1.490711985 + 2 = 3.490711985 x2 = 3.490711985 Simplifying x2 = 3.490711985 Take the square root of each side: x = {-1.868344718, 1.868344718}Subproblem 2
x2 + -2 = -1.490711985 Simplifying x2 + -2 = -1.490711985 Reorder the terms: -2 + x2 = -1.490711985 Solving -2 + x2 = -1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -1.490711985 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -1.490711985 + 2 x2 = -1.490711985 + 2 Combine like terms: -1.490711985 + 2 = 0.509288015 x2 = 0.509288015 Simplifying x2 = 0.509288015 Take the square root of each side: x = {-0.71364418, 0.71364418}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.868344718, 1.868344718, -0.71364418, 0.71364418}
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