4n^2-7=-7n

Simple and best practice solution for 4n^2-7=-7n 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 4n^2-7=-7n equation:


Simplifying
4n2 + -7 = -7n

Reorder the terms:
-7 + 4n2 = -7n

Solving
-7 + 4n2 = -7n

Solving for variable 'n'.

Reorder the terms:
-7 + 7n + 4n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-7 + 7n + 4n2 = 0

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

Divide each side by '4'.
-1.75 + 1.75n + n2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 1.75n + 1.75 + n2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 1.75n + n2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 1.75n + n2 = 0 + 1.75
1.75n + n2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
1.75n + n2 = 1.75

The n term is 1.75n.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75n + 0.765625 + n2 = 1.75 + 0.765625

Reorder the terms:
0.765625 + 1.75n + n2 = 1.75 + 0.765625

Combine like terms: 1.75 + 0.765625 = 2.515625
0.765625 + 1.75n + n2 = 2.515625

Factor a perfect square on the left side:
(n + 0.875)(n + 0.875) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(n + 0.875) equal to 1.586072193 and -1.586072193.

Subproblem 1

n + 0.875 = 1.586072193 Simplifying n + 0.875 = 1.586072193 Reorder the terms: 0.875 + n = 1.586072193 Solving 0.875 + n = 1.586072193 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + n = 1.586072193 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + n = 1.586072193 + -0.875 n = 1.586072193 + -0.875 Combine like terms: 1.586072193 + -0.875 = 0.711072193 n = 0.711072193 Simplifying n = 0.711072193

Subproblem 2

n + 0.875 = -1.586072193 Simplifying n + 0.875 = -1.586072193 Reorder the terms: 0.875 + n = -1.586072193 Solving 0.875 + n = -1.586072193 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + n = -1.586072193 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + n = -1.586072193 + -0.875 n = -1.586072193 + -0.875 Combine like terms: -1.586072193 + -0.875 = -2.461072193 n = -2.461072193 Simplifying n = -2.461072193

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.711072193, -2.461072193}

See similar equations:

| 30/20=x/4 | | 5c+9=4z-1 | | 3+4(x-5)=34 | | 9(x+1)+4(x+1)=6x-6 | | -6+11=-5-2 | | x^7-6x^5+2x^4-5=0 | | 2p-3=11 | | 3+7n=1+6n | | ln^3x=5 | | 5k^2=6-k | | (x+1)+(y-2)=7 | | 4x+25=8x+37 | | 16-2w=5w+9 | | 8x=215-13x | | 65+7x+5x-5=180 | | 5x^3+2x^2-x=0 | | 4y=12x-5 | | 7p+14=p-4 | | 6n^2-8=-93 | | -132=-7d-4d | | 8+3e^3x=26 | | 25a^2+8=108 | | 3h+12h=18 | | -5+3m=2m+2 | | X/7=10/2 | | 70+x+80+x+40=180 | | 8+3e=26 | | n^2=6+n | | 0=-4u^2-31u-50 | | X(5-x)=8-(x+3) | | 7-3x=-12 | | 3k+12k=60 |

Equations solver categories