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Simplifying x4 + -14x2 + 14 = 0 Reorder the terms: 14 + -14x2 + x4 = 0 Solving 14 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -14x2 + -14 + x4 = 0 + -14 Reorder the terms: 14 + -14 + -14x2 + x4 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -14x2 + x4 = 0 + -14 -14x2 + x4 = 0 + -14 Combine like terms: 0 + -14 = -14 -14x2 + x4 = -14 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = -14 + 49 Reorder the terms: 49 + -14x2 + x4 = -14 + 49 Combine like terms: -14 + 49 = 35 49 + -14x2 + x4 = 35 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x2 + -7) equal to 5.916079783 and -5.916079783.Subproblem 1
x2 + -7 = 5.916079783 Simplifying x2 + -7 = 5.916079783 Reorder the terms: -7 + x2 = 5.916079783 Solving -7 + x2 = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 5.916079783 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 5.916079783 + 7 x2 = 5.916079783 + 7 Combine like terms: 5.916079783 + 7 = 12.916079783 x2 = 12.916079783 Simplifying x2 = 12.916079783 Take the square root of each side: x = {-3.593894793, 3.593894793}Subproblem 2
x2 + -7 = -5.916079783 Simplifying x2 + -7 = -5.916079783 Reorder the terms: -7 + x2 = -5.916079783 Solving -7 + x2 = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -5.916079783 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -5.916079783 + 7 x2 = -5.916079783 + 7 Combine like terms: -5.916079783 + 7 = 1.083920217 x2 = 1.083920217 Simplifying x2 = 1.083920217 Take the square root of each side: x = {-1.041114891, 1.041114891}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.593894793, 3.593894793, -1.041114891, 1.041114891}
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