4x^4-12x^2+3=0

Simple and best practice solution for 4x^4-12x^2+3=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^4-12x^2+3=0 equation:


Simplifying
4x4 + -12x2 + 3 = 0

Reorder the terms:
3 + -12x2 + 4x4 = 0

Solving
3 + -12x2 + 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'.
0.75 + -3x2 + x4 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -3x2 + -0.75 + x4 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -3x2 + x4 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -3x2 + x4 = 0 + -0.75
-3x2 + x4 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-3x2 + x4 = -0.75

The x term is -3x2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x2 + 2.25 + x4 = -0.75 + 2.25

Reorder the terms:
2.25 + -3x2 + x4 = -0.75 + 2.25

Combine like terms: -0.75 + 2.25 = 1.5
2.25 + -3x2 + x4 = 1.5

Factor a perfect square on the left side:
(x2 + -1.5)(x2 + -1.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x2 + -1.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x2 + -1.5 = 1.224744871 Simplifying x2 + -1.5 = 1.224744871 Reorder the terms: -1.5 + x2 = 1.224744871 Solving -1.5 + x2 = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.224744871 + 1.5 x2 = 1.224744871 + 1.5 Combine like terms: 1.224744871 + 1.5 = 2.724744871 x2 = 2.724744871 Simplifying x2 = 2.724744871 Take the square root of each side: x = {-1.650680124, 1.650680124}

Subproblem 2

x2 + -1.5 = -1.224744871 Simplifying x2 + -1.5 = -1.224744871 Reorder the terms: -1.5 + x2 = -1.224744871 Solving -1.5 + x2 = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.224744871 + 1.5 x2 = -1.224744871 + 1.5 Combine like terms: -1.224744871 + 1.5 = 0.275255129 x2 = 0.275255129 Simplifying x2 = 0.275255129 Take the square root of each side: x = {-0.524647624, 0.524647624}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.650680124, 1.650680124, -0.524647624, 0.524647624}

See similar equations:

| 45=2x-5 | | -6=9+a+a+4 | | 6-8x+9x-6=3-9x+9x-6 | | 2x+3(4x-6)=24 | | n+10= | | y+4y+1=7(y-1) | | 6-8x+9x=3-9x-6 | | 20+m=30+m | | 18x^2-64x-36=0 | | 2a=4(a-5) | | -6a-7=17 | | (y-2)2+14=8y-3y | | 5x+3=5x-9 | | 10h-12=78 | | 6(b-3)=4(b-4) | | 8x-7+2x=33 | | 8x-2x-10=2 | | 7m+10=59 | | (6x-5)(12y+14)=0 | | 6m+7=61 | | 3(n-3)=4n | | -8+6t=2+4t | | B-(1-2b)+b-3=-4 | | 2(w+5)+4w=32 | | 6x^2(x^2+7)-32x(x^2+7)+40(x^2+7)= | | 13-5y+2y=28 | | 22x+7=223 | | 10.8x=6-24 | | 10.8=6y-24 | | 4X+7Y=53 | | 2(w+5)+w=32 | | 780+656= |

Equations solver categories