x^4-23x^2+1=0

Simple and best practice solution for x^4-23x^2+1=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^4-23x^2+1=0 equation:


Simplifying
x4 + -23x2 + 1 = 0

Reorder the terms:
1 + -23x2 + x4 = 0

Solving
1 + -23x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -23x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -23x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -23x2 + x4 = 0 + -1
-23x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-23x2 + x4 = -1

The x term is -23x2.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x2 + 132.25 + x4 = -1 + 132.25

Reorder the terms:
132.25 + -23x2 + x4 = -1 + 132.25

Combine like terms: -1 + 132.25 = 131.25
132.25 + -23x2 + x4 = 131.25

Factor a perfect square on the left side:
(x2 + -11.5)(x2 + -11.5) = 131.25

Calculate the square root of the right side: 11.456439237

Break this problem into two subproblems by setting 
(x2 + -11.5) equal to 11.456439237 and -11.456439237.

Subproblem 1

x2 + -11.5 = 11.456439237 Simplifying x2 + -11.5 = 11.456439237 Reorder the terms: -11.5 + x2 = 11.456439237 Solving -11.5 + x2 = 11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x2 = 11.456439237 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = 11.456439237 + 11.5 x2 = 11.456439237 + 11.5 Combine like terms: 11.456439237 + 11.5 = 22.956439237 x2 = 22.956439237 Simplifying x2 = 22.956439237 Take the square root of each side: x = {-4.791287847, 4.791287847}

Subproblem 2

x2 + -11.5 = -11.456439237 Simplifying x2 + -11.5 = -11.456439237 Reorder the terms: -11.5 + x2 = -11.456439237 Solving -11.5 + x2 = -11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x2 = -11.456439237 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = -11.456439237 + 11.5 x2 = -11.456439237 + 11.5 Combine like terms: -11.456439237 + 11.5 = 0.043560763 x2 = 0.043560763 Simplifying x2 = 0.043560763 Take the square root of each side: x = {-0.208712153, 0.208712153}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.791287847, 4.791287847, -0.208712153, 0.208712153}

See similar equations:

| 6x+5=-100-9k | | 8v=2(2v+2) | | 3-6k=13-8k | | x-12=4(x-2) | | -8b+7=4b-5 | | 59-4x=11-10x | | 4x+12=-12-2x | | 7y-2=4y-1 | | x=1.891*log(2.358+0.679*x) | | S+7=10 | | 3.2x+4=13.6 | | 3.2+4=13.6 | | -3z+-3c=2c-8 | | -15+10-15=4z+3 | | 11+3x=-1 | | -16(7c-1)-2=110c+16 | | 5(a-4)=25 | | 2(1-5)=3(5x-1) | | (x+3)dy=ydx | | 7y+5=5 | | 36+8t=9t+36 | | 69x+3y=0 | | 5y-10=2y-22 | | 3y+8=26 | | 3(x+2)=-3x-6 | | 3x-15=5(2x+3) | | -9n+4=-8n-1 | | -9n+4=-8n-2 | | x+(x-3)=147 | | 2x^2+7y^2=42 | | -3+10=13x-2-12x | | x^2+18x+69=0 |

Equations solver categories