4x^4-3x^2-19=0

Simple and best practice solution for 4x^4-3x^2-19=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 4x^4-3x^2-19=0 equation: 


Simplifying
4x4 + -3x2 + -19 = 0

Reorder the terms:
-19 + -3x2 + 4x4 = 0

Solving
-19 + -3x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-4.75 + -0.75x2 + x4 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + -0.75x2 + 4.75 + x4 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + -0.75x2 + x4 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + -0.75x2 + x4 = 0 + 4.75
-0.75x2 + x4 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
-0.75x2 + x4 = 4.75

The x term is -0.75x2.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x2 + 0.140625 + x4 = 4.75 + 0.140625

Reorder the terms:
0.140625 + -0.75x2 + x4 = 4.75 + 0.140625

Combine like terms: 4.75 + 0.140625 = 4.890625
0.140625 + -0.75x2 + x4 = 4.890625

Factor a perfect square on the left side:
(x2 + -0.375)(x2 + -0.375) = 4.890625

Calculate the square root of the right side: 2.211475752

Break this problem into two subproblems by setting 
(x2 + -0.375) equal to 2.211475752 and -2.211475752.


Subproblem 1
x2 + -0.375 = 2.211475752

Simplifying
x2 + -0.375 = 2.211475752

Reorder the terms:
-0.375 + x2 = 2.211475752

Solving
-0.375 + x2 = 2.211475752

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x2 = 2.211475752 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = 2.211475752 + 0.375
x2 = 2.211475752 + 0.375

Combine like terms: 2.211475752 + 0.375 = 2.586475752
x2 = 2.586475752

Simplifying
x2 = 2.586475752

Take the square root of each side:
x = {-1.608252391, 1.608252391}


Subproblem 2
x2 + -0.375 = -2.211475752

Simplifying
x2 + -0.375 = -2.211475752

Reorder the terms:
-0.375 + x2 = -2.211475752

Solving
-0.375 + x2 = -2.211475752

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x2 = -2.211475752 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = -2.211475752 + 0.375
x2 = -2.211475752 + 0.375

Combine like terms: -2.211475752 + 0.375 = -1.836475752
x2 = -1.836475752

Simplifying
x2 = -1.836475752

Reorder the terms:
1.836475752 + x2 = -1.836475752 + 1.836475752

Combine like terms: -1.836475752 + 1.836475752 = 0.000000000
1.836475752 + 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:

| -5(x-4)+3x-5=-1 | | 25=.49r | | n*n+1*n+2=57 | | 1-7i= | | 2x^2-bx-3=0 | | 3x-1=8+7 | | 96=-4x-7x-3 | | -3x+2(-4x-18)=-135 | | 63-(3x+9)=3(x+4)+x | | 54-10x=-54-6x | | (-9-12)n=8-4n | | 3y+21x=-15 | | 25x^5y^2-5x^4y^3= | | (16)x(-18)= | | FaZe+4=3 | | 5a+7=10 | | 20(c)+100=1140 | | x^2+12x=10x | | (16)(-18)= | | 9x+1512y=714-15 | | 7.7p=76.23 | | 2x^4-2x^3+6x^2-5x+1=0 | | 5(2T-1)+4t=10-10 | | 6y=9x+6 | | 40=-5(x+3)(x-6) | | 2x+20+x+40=180 | | 7x+3(2x-8)=119 | | 115(m)+500=2685 | | -3(k-4)=-6t | | -3=4X+6-Z | | x^2+17=2(3x-2) | | 11y=5x-22 |

Equations solver categories