x^4-x^2+0.24=0

Simple and best practice solution for x^4-x^2+0.24=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-x^2+0.24=0 equation: 


Simplifying
x4 + -1x2 + 0.24 = 0

Reorder the terms:
0.24 + -1x2 + x4 = 0

Solving
0.24 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.24' to each side of the equation.
0.24 + -1x2 + -0.24 + x4 = 0 + -0.24

Reorder the terms:
0.24 + -0.24 + -1x2 + x4 = 0 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + -1x2 + x4 = 0 + -0.24
-1x2 + x4 = 0 + -0.24

Combine like terms: 0 + -0.24 = -0.24
-1x2 + x4 = -0.24

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = -0.24 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = -0.24 + 0.25

Combine like terms: -0.24 + 0.25 = 0.01
0.25 + -1x2 + x4 = 0.01

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.1 and -0.1.


Subproblem 1
x2 + -0.5 = 0.1

Simplifying
x2 + -0.5 = 0.1

Reorder the terms:
-0.5 + x2 = 0.1

Solving
-0.5 + x2 = 0.1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 0.1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0.1 + 0.5
x2 = 0.1 + 0.5

Combine like terms: 0.1 + 0.5 = 0.6
x2 = 0.6

Simplifying
x2 = 0.6

Take the square root of each side:
x = {-0.774596669, 0.774596669}


Subproblem 2
x2 + -0.5 = -0.1

Simplifying
x2 + -0.5 = -0.1

Reorder the terms:
-0.5 + x2 = -0.1

Solving
-0.5 + x2 = -0.1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = -0.1 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -0.1 + 0.5
x2 = -0.1 + 0.5

Combine like terms: -0.1 + 0.5 = 0.4
x2 = 0.4

Simplifying
x2 = 0.4

Take the square root of each side:
x = {-0.632455532, 0.632455532}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.774596669, 0.774596669, -0.632455532, 0.632455532}

See similar equations:

| -5-3x+2=-18+11-3x | | 5+9=149 | | -4-7(4-6r)=40+6r | | 37/40= | | 37/4= | | 6m+7-8=-19 | | 5(2b+11)= | | -2(-2+4x)=4+5x | | -4(-3w+9)-6w=2(w-8)-2 | | 12.26=s-6.69 | | 8c+2-c+6= | | 3x=(7y-2) | | -12(m-6)=-8(1+2m) | | -12(m-6)=8(1+2m) | | 16x-24=120 | | (2+5x+5x^2+8x^3)+(7-5x+5x^2-8x^3)= | | -7v+5(v+7)=7 | | 3/20= | | x^2+x-4= | | 2m+3p-p+m= | | -9u+18=-6(u-7) | | -23-143= | | -3(-18)+6y=-18 | | x^4-x^2+0.245=0 | | 13/20= | | 4(n+4)=-12(n-4) | | 13/65= | | 10p-2-p-14=6p-5-2p-6 | | (7w+6v)(7w-6v)= | | x^4-0.56x^2+0.0574=0 | | -2-2x+6-4x=-4-5x+8 | | 6y-15= |

Equations solver categories