x^4-10x^2+7=0

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Solution for x^4-10x^2+7=0 equation:


Simplifying
x4 + -10x2 + 7 = 0

Reorder the terms:
7 + -10x2 + x4 = 0

Solving
7 + -10x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -10x2 + -7 + x4 = 0 + -7

Reorder the terms:
7 + -7 + -10x2 + x4 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -10x2 + x4 = 0 + -7
-10x2 + x4 = 0 + -7

Combine like terms: 0 + -7 = -7
-10x2 + x4 = -7

The x term is -10x2.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x2 + 25 + x4 = -7 + 25

Reorder the terms:
25 + -10x2 + x4 = -7 + 25

Combine like terms: -7 + 25 = 18
25 + -10x2 + x4 = 18

Factor a perfect square on the left side:
(x2 + -5)(x2 + -5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x2 + -5) equal to 4.242640687 and -4.242640687.

Subproblem 1

x2 + -5 = 4.242640687 Simplifying x2 + -5 = 4.242640687 Reorder the terms: -5 + x2 = 4.242640687 Solving -5 + x2 = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 4.242640687 + 5 x2 = 4.242640687 + 5 Combine like terms: 4.242640687 + 5 = 9.242640687 x2 = 9.242640687 Simplifying x2 = 9.242640687 Take the square root of each side: x = {-3.040171161, 3.040171161}

Subproblem 2

x2 + -5 = -4.242640687 Simplifying x2 + -5 = -4.242640687 Reorder the terms: -5 + x2 = -4.242640687 Solving -5 + x2 = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -4.242640687 + 5 x2 = -4.242640687 + 5 Combine like terms: -4.242640687 + 5 = 0.757359313 x2 = 0.757359313 Simplifying x2 = 0.757359313 Take the square root of each side: x = {-0.870263933, 0.870263933}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.040171161, 3.040171161, -0.870263933, 0.870263933}

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