x^4-41.4236x^2+1=0

Simple and best practice solution for x^4-41.4236x^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^4-41.4236x^2+1=0 equation:


Simplifying
x4 + -41.4236x2 + 1 = 0

Reorder the terms:
1 + -41.4236x2 + x4 = 0

Solving
1 + -41.4236x2 + 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 + -41.4236x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -41.4236x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -41.4236x2 + x4 = 0 + -1
-41.4236x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-41.4236x2 + x4 = -1

The x term is -41.4236x2.  Take half its coefficient (-20.7118).
Square it (428.9786592) and add it to both sides.

Add '428.9786592' to each side of the equation.
-41.4236x2 + 428.9786592 + x4 = -1 + 428.9786592

Reorder the terms:
428.9786592 + -41.4236x2 + x4 = -1 + 428.9786592

Combine like terms: -1 + 428.9786592 = 427.9786592
428.9786592 + -41.4236x2 + x4 = 427.9786592

Factor a perfect square on the left side:
(x2 + -20.7118)(x2 + -20.7118) = 427.9786592

Calculate the square root of the right side: 20.687645086

Break this problem into two subproblems by setting 
(x2 + -20.7118) equal to 20.687645086 and -20.687645086.

Subproblem 1

x2 + -20.7118 = 20.687645086 Simplifying x2 + -20.7118 = 20.687645086 Reorder the terms: -20.7118 + x2 = 20.687645086 Solving -20.7118 + x2 = 20.687645086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.7118' to each side of the equation. -20.7118 + 20.7118 + x2 = 20.687645086 + 20.7118 Combine like terms: -20.7118 + 20.7118 = 0.0000 0.0000 + x2 = 20.687645086 + 20.7118 x2 = 20.687645086 + 20.7118 Combine like terms: 20.687645086 + 20.7118 = 41.399445086 x2 = 41.399445086 Simplifying x2 = 41.399445086 Take the square root of each side: x = {-6.434240055, 6.434240055}

Subproblem 2

x2 + -20.7118 = -20.687645086 Simplifying x2 + -20.7118 = -20.687645086 Reorder the terms: -20.7118 + x2 = -20.687645086 Solving -20.7118 + x2 = -20.687645086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.7118' to each side of the equation. -20.7118 + 20.7118 + x2 = -20.687645086 + 20.7118 Combine like terms: -20.7118 + 20.7118 = 0.0000 0.0000 + x2 = -20.687645086 + 20.7118 x2 = -20.687645086 + 20.7118 Combine like terms: -20.687645086 + 20.7118 = 0.024154914 x2 = 0.024154914 Simplifying x2 = 0.024154914 Take the square root of each side: x = {-0.155418512, 0.155418512}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-6.434240055, 6.434240055, -0.155418512, 0.155418512}

See similar equations:

| -100x^2+1300x-3600=0 | | 8+2x(5)=-0.8(6)+12 | | t=3t-15 | | 8(x-8)-4x=-36 | | a^2-2a-36=0 | | 38=-1-3a | | 12.9=3.2-x/1.8 | | 6-12a/4a^2-1 | | 0.4x+5+0.2x=17 | | 55=x-6 | | 33=x-45 | | (4/3)(x-2)-(1/2)=2((3/4)x-4) | | 8+2x(5)= | | 7y=385 | | 10/20a-35 | | 30-3(x+2)=9 | | 10/201-35 | | 12=-1.5x^2+9x | | -2x+2/3+3/2/3=11/2/3 | | 7x^4-5x^3+x^2-4x+2=0 | | 3=.2x+2.5 | | (-12x)(2/3x^2)(-4y) | | (2x+1)(x+6)=2x(x+4)+81 | | v=1/3*3.14*1/9*3 | | 2/7x-5=15 | | 24/30=x/100 | | 120n^2+152n-448=0 | | 3y=5x-1 | | 2/2/5w=21/3/5 | | -6x^2+8x+5=0 | | Log(y)=1.373866 | | -6t=1.8 |

Equations solver categories