2x^4+5x^2=1

Simple and best practice solution for 2x^4+5x^2=1 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 2x^4+5x^2=1 equation:


Simplifying
2x4 + 5x2 = 1

Reorder the terms:
5x2 + 2x4 = 1

Solving
5x2 + 2x4 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 5x2 + 2x4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 5x2 + 2x4 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + 2.5x2 + x4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2.5x2 + 0.5 + x4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2.5x2 + x4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2.5x2 + x4 = 0 + 0.5
2.5x2 + x4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2.5x2 + x4 = 0.5

The x term is 2.5x2.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x2 + 1.5625 + x4 = 0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x2 + x4 = 0.5 + 1.5625

Combine like terms: 0.5 + 1.5625 = 2.0625
1.5625 + 2.5x2 + x4 = 2.0625

Factor a perfect square on the left side:
(x2 + 1.25)(x2 + 1.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x2 + 1.25) equal to 1.436140662 and -1.436140662.

Subproblem 1

x2 + 1.25 = 1.436140662 Simplifying x2 + 1.25 = 1.436140662 Reorder the terms: 1.25 + x2 = 1.436140662 Solving 1.25 + x2 = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x2 = 1.436140662 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x2 = 1.436140662 + -1.25 x2 = 1.436140662 + -1.25 Combine like terms: 1.436140662 + -1.25 = 0.186140662 x2 = 0.186140662 Simplifying x2 = 0.186140662 Take the square root of each side: x = {-0.431440218, 0.431440218}

Subproblem 2

x2 + 1.25 = -1.436140662 Simplifying x2 + 1.25 = -1.436140662 Reorder the terms: 1.25 + x2 = -1.436140662 Solving 1.25 + x2 = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x2 = -1.436140662 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x2 = -1.436140662 + -1.25 x2 = -1.436140662 + -1.25 Combine like terms: -1.436140662 + -1.25 = -2.686140662 x2 = -2.686140662 Simplifying x2 = -2.686140662 Reorder the terms: 2.686140662 + x2 = -2.686140662 + 2.686140662 Combine like terms: -2.686140662 + 2.686140662 = 0.000000000 2.686140662 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

See similar equations:

| -x^2+26=3x^2-52 | | X/3-2/6=4/12 | | 385n+85=c | | (x+7)-(x+4)=30 | | r^6/r | | (x+3)-(x+4)=30 | | 2(x+7)=3(7-x) | | x-3x+8= | | (x-4)*(x+3)=20 | | (x-4)*(x+3)=93 | | 4x+y=894.7 | | t-16=0 | | -5(2t+1)=-35 | | 3(f-10)=-24 | | 64+4=44a | | 7q=133 | | 2(3s+3)=18 | | 7a^2-3a-4=0 | | 7x+x=1000 | | 2tan(x)-3=0 | | 2n-1/3 | | 145-z=106 | | 16-3p=0.666666666666666666666666666666666666666666666666666666666666666p+5 | | (2y-4.5)=1.5y | | x+5y-3z=-3 | | x^3-7x=5 | | 9a^2+19a+2=0 | | -4a-2a+11=6a-3 | | (45+3x)=60 | | x-27=56 | | 2(t-3)+2=2(2t-4) | | 1x+1+x+2=393 |

Equations solver categories