n^2+8n-7=0

Simple and best practice solution for n^2+8n-7=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 n^2+8n-7=0 equation:


Simplifying
n2 + 8n + -7 = 0

Reorder the terms:
-7 + 8n + n2 = 0

Solving
-7 + 8n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 8n + 7 + n2 = 0 + 7

Reorder the terms:
-7 + 7 + 8n + n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 8n + n2 = 0 + 7
8n + n2 = 0 + 7

Combine like terms: 0 + 7 = 7
8n + n2 = 7

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

Add '16' to each side of the equation.
8n + 16 + n2 = 7 + 16

Reorder the terms:
16 + 8n + n2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + 8n + n2 = 23

Factor a perfect square on the left side:
(n + 4)(n + 4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(n + 4) equal to 4.795831523 and -4.795831523.

Subproblem 1

n + 4 = 4.795831523 Simplifying n + 4 = 4.795831523 Reorder the terms: 4 + n = 4.795831523 Solving 4 + n = 4.795831523 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 + n = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + n = 4.795831523 + -4 n = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 n = 0.795831523 Simplifying n = 0.795831523

Subproblem 2

n + 4 = -4.795831523 Simplifying n + 4 = -4.795831523 Reorder the terms: 4 + n = -4.795831523 Solving 4 + n = -4.795831523 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 + n = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + n = -4.795831523 + -4 n = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 n = -8.795831523 Simplifying n = -8.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.795831523, -8.795831523}

See similar equations:

| 7w^2+3=-10w | | 36=16x-12x | | 4(2x)=40 | | 3x^2+x-0.5=0 | | 2(3x)=36 | | 10x+6y=16 | | -7x^2-18x+0=0 | | 2z-67=-21 | | 8-(-4)+5=12 | | 7n+3-5n=3n-6 | | V=3.14v^2h | | (25)(7)+x=175 | | -3x+6x=0 | | 0=5x^2-64x-13 | | 18+5=48 | | x-29=15 | | .5(12x-8)=9x-18 | | 5x-3-2x=2(x-4) | | 3(x+2)=5(x-1)+5 | | 0=2a^2+7a+3 | | 4(5y-3)-(8y+5)= | | 2x+5(6x-4)=44 | | 40(25+x)=1 | | 8x-14=3x-6 | | m+90=150 | | -16x^2+324=0 | | 9x+6=6x+4 | | 0=-15m^2+60 | | 8(4+x)=360 | | 10x+7=8x-6 | | 21-12=3(x-8) | | 2x-(x-1)=3+x |

Equations solver categories