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Simplifying x4 = 6x2 + -7 Reorder the terms: x4 = -7 + 6x2 Solving x4 = -7 + 6x2 Solving for variable 'x'. Reorder the terms: 7 + -6x2 + x4 = -7 + 6x2 + 7 + -6x2 Reorder the terms: 7 + -6x2 + x4 = -7 + 7 + 6x2 + -6x2 Combine like terms: -7 + 7 = 0 7 + -6x2 + x4 = 0 + 6x2 + -6x2 7 + -6x2 + x4 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 7 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6x2 + -7 + x4 = 0 + -7 Reorder the terms: 7 + -7 + -6x2 + x4 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x2 + x4 = 0 + -7 -6x2 + x4 = 0 + -7 Combine like terms: 0 + -7 = -7 -6x2 + x4 = -7 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -7 + 9 Reorder the terms: 9 + -6x2 + x4 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6x2 + x4 = 2 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x2 + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
x2 + -3 = 1.414213562 Simplifying x2 + -3 = 1.414213562 Reorder the terms: -3 + x2 = 1.414213562 Solving -3 + x2 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 1.414213562 + 3 x2 = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 x2 = 4.414213562 Simplifying x2 = 4.414213562 Take the square root of each side: x = {-2.10100299, 2.10100299}Subproblem 2
x2 + -3 = -1.414213562 Simplifying x2 + -3 = -1.414213562 Reorder the terms: -3 + x2 = -1.414213562 Solving -3 + x2 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -1.414213562 + 3 x2 = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 x2 = 1.585786438 Simplifying x2 = 1.585786438 Take the square root of each side: x = {-1.259280127, 1.259280127}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.10100299, 2.10100299, -1.259280127, 1.259280127}
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