0=x^4-8x^2+5

Simple and best practice solution for 0=x^4-8x^2+5 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 0=x^4-8x^2+5 equation:


Simplifying
0 = x4 + -8x2 + 5

Reorder the terms:
0 = 5 + -8x2 + x4

Solving
0 = 5 + -8x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + 8x2 + -1x4 = 5 + -8x2 + x4 + -5 + 8x2 + -1x4

Reorder the terms:
-5 + 8x2 + -1x4 = 5 + -5 + -8x2 + 8x2 + x4 + -1x4

Combine like terms: 5 + -5 = 0
-5 + 8x2 + -1x4 = 0 + -8x2 + 8x2 + x4 + -1x4
-5 + 8x2 + -1x4 = -8x2 + 8x2 + x4 + -1x4

Combine like terms: -8x2 + 8x2 = 0
-5 + 8x2 + -1x4 = 0 + x4 + -1x4
-5 + 8x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-5 + 8x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -8x2 + x4 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8x2 + -5 + x4 = 0 + -5

Reorder the terms:
5 + -5 + -8x2 + x4 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x2 + x4 = 0 + -5
-8x2 + x4 = 0 + -5

Combine like terms: 0 + -5 = -5
-8x2 + x4 = -5

The x term is -8x2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x2 + 16 + x4 = -5 + 16

Reorder the terms:
16 + -8x2 + x4 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8x2 + x4 = 11

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x2 + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1

x2 + -4 = 3.31662479 Simplifying x2 + -4 = 3.31662479 Reorder the terms: -4 + x2 = 3.31662479 Solving -4 + x2 = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.31662479 + 4 x2 = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x2 = 7.31662479 Simplifying x2 = 7.31662479 Take the square root of each side: x = {-2.704926023, 2.704926023}

Subproblem 2

x2 + -4 = -3.31662479 Simplifying x2 + -4 = -3.31662479 Reorder the terms: -4 + x2 = -3.31662479 Solving -4 + x2 = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.31662479 + 4 x2 = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x2 = 0.68337521 Simplifying x2 = 0.68337521 Take the square root of each side: x = {-0.826665114, 0.826665114}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.704926023, 2.704926023, -0.826665114, 0.826665114}

See similar equations:

| 3a^2+7a=0 | | (-4x)=8 | | .7x-2.2=.6 | | 7f+16=3f+48 | | (x-1)+(x-2)-(x-3)=-4 | | 2x-3=6x-5 | | 3x^2+21x-30=0 | | 2(x+8)=32 | | 184=4(5k+6) | | -408=12(-9x+2) | | 6x-3=10-6(2-x) | | 2X^3-14X^2+24X=0 | | 4=2x+6 | | 4v+7(v-6)=-97 | | 18+4(3x-7)=-7 | | 2(y-3)-5y=-3(y+3) | | (x+1)(y+1)=2xy | | 3x+4y= | | x^2-25x-12=0 | | 6(2x+3)+4= | | (X-1)(x+1)=5(x-1) | | q=4g+4u | | 3x+7=5x+23 | | x+y=xy-1 | | (4x-4)-3x=1 | | 4r-8r+9+r= | | 16-3x=-14 | | 8x+3(x-5)=4(x+2)-3 | | 20t^2-13t-15=0 | | q=4q+4u | | 116=8(1+4a)-5a | | 12y^2-33y+21= |

Equations solver categories