n^4=8n^2-9

Simple and best practice solution for n^4=8n^2-9 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 n^4=8n^2-9 equation:


Simplifying
n4 = 8n2 + -9

Reorder the terms:
n4 = -9 + 8n2

Solving
n4 = -9 + 8n2

Solving for variable 'n'.

Reorder the terms:
9 + -8n2 + n4 = -9 + 8n2 + 9 + -8n2

Reorder the terms:
9 + -8n2 + n4 = -9 + 9 + 8n2 + -8n2

Combine like terms: -9 + 9 = 0
9 + -8n2 + n4 = 0 + 8n2 + -8n2
9 + -8n2 + n4 = 8n2 + -8n2

Combine like terms: 8n2 + -8n2 = 0
9 + -8n2 + n4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8n2 + -9 + n4 = 0 + -9

Reorder the terms:
9 + -9 + -8n2 + n4 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8n2 + n4 = 0 + -9
-8n2 + n4 = 0 + -9

Combine like terms: 0 + -9 = -9
-8n2 + n4 = -9

The n term is -8n2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n2 + 16 + n4 = -9 + 16

Reorder the terms:
16 + -8n2 + n4 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8n2 + n4 = 7

Factor a perfect square on the left side:
(n2 + -4)(n2 + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n2 + -4) equal to 2.645751311 and -2.645751311.

Subproblem 1

n2 + -4 = 2.645751311 Simplifying n2 + -4 = 2.645751311 Reorder the terms: -4 + n2 = 2.645751311 Solving -4 + n2 = 2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n2 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + n2 = 2.645751311 + 4 n2 = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 n2 = 6.645751311 Simplifying n2 = 6.645751311 Take the square root of each side: n = {-2.577935475, 2.577935475}

Subproblem 2

n2 + -4 = -2.645751311 Simplifying n2 + -4 = -2.645751311 Reorder the terms: -4 + n2 = -2.645751311 Solving -4 + n2 = -2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n2 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + n2 = -2.645751311 + 4 n2 = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 n2 = 1.354248689 Simplifying n2 = 1.354248689 Take the square root of each side: n = {-1.163721912, 1.163721912}

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-2.577935475, 2.577935475, -1.163721912, 1.163721912}

See similar equations:

| 108.5-x=53.9 | | v^2=u^2+2(as) | | 14m=-280 | | -2x+14=9(x-7) | | 4-4x+2=5x-3 | | axb=65 | | (6x+80)=4x+6x | | .04(y-6)+.10y=.12y-.01(40) | | 162=2(9+x)+2x | | -2w=-15.2 | | -6g+36=26 | | 2(3x+6)+8=8+3x | | 5=3.5a | | (3/5 | | -5(y-2)=-8y+22 | | 5x+4y=-15 | | -5(x+6)-5=-35 | | 4x-3+5=18 | | -5x-35=35 | | -1/6*-2/5 | | F(x)=.825x | | -1/6x-2/5 | | 7(5+c)=6[c-3] | | 3x+4y=2x+10y | | 5/3b=15 | | 2v-39=9(v-2) | | 16+8[z-2]=7z+1 | | (4x^8-6x^5)(-21x+2)= | | 16-3p=.667p+5 | | 48-(2c+3)=4(c+6)+6 | | 8w=5w-18 | | 5z=13-6z |

Equations solver categories