9n^2=4+7n

Simple and best practice solution for 9n^2=4+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 9n^2=4+7n equation:


Simplifying
9n2 = 4 + 7n

Solving
9n2 = 4 + 7n

Solving for variable 'n'.

Reorder the terms:
-4 + -7n + 9n2 = 4 + 7n + -4 + -7n

Reorder the terms:
-4 + -7n + 9n2 = 4 + -4 + 7n + -7n

Combine like terms: 4 + -4 = 0
-4 + -7n + 9n2 = 0 + 7n + -7n
-4 + -7n + 9n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-4 + -7n + 9n2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.7777777778n + n2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.7777777778n + 0.4444444444 + n2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.7777777778n + n2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.7777777778n + n2 = 0 + 0.4444444444
-0.7777777778n + n2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.7777777778n + n2 = 0.4444444444

The n term is -0.7777777778n.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778n + 0.1512345679 + n2 = 0.4444444444 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778n + n2 = 0.4444444444 + 0.1512345679

Combine like terms: 0.4444444444 + 0.1512345679 = 0.5956790123
0.1512345679 + -0.7777777778n + n2 = 0.5956790123

Factor a perfect square on the left side:
(n + -0.3888888889)(n + -0.3888888889) = 0.5956790123

Calculate the square root of the right side: 0.771802444

Break this problem into two subproblems by setting 
(n + -0.3888888889) equal to 0.771802444 and -0.771802444.

Subproblem 1

n + -0.3888888889 = 0.771802444 Simplifying n + -0.3888888889 = 0.771802444 Reorder the terms: -0.3888888889 + n = 0.771802444 Solving -0.3888888889 + n = 0.771802444 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + n = 0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = 0.771802444 + 0.3888888889 n = 0.771802444 + 0.3888888889 Combine like terms: 0.771802444 + 0.3888888889 = 1.1606913329 n = 1.1606913329 Simplifying n = 1.1606913329

Subproblem 2

n + -0.3888888889 = -0.771802444 Simplifying n + -0.3888888889 = -0.771802444 Reorder the terms: -0.3888888889 + n = -0.771802444 Solving -0.3888888889 + n = -0.771802444 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + n = -0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = -0.771802444 + 0.3888888889 n = -0.771802444 + 0.3888888889 Combine like terms: -0.771802444 + 0.3888888889 = -0.3829135551 n = -0.3829135551 Simplifying n = -0.3829135551

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.1606913329, -0.3829135551}

See similar equations:

| x-(0.03x)=4694 | | 8x-9x=10x+2 | | 90x+40x=70 | | 11-8x=44-29x | | 2x^3-3x^2-36x+7=0 | | 9x+4x=7 | | x^2+35x+60=10260 | | 113-7x=20x+17 | | 4x-2=8x-14 | | -56-2x=5x+12 | | 33-5x=40x+23 | | 21n^2=25-20n | | 4x+10=66-3x | | V^2+6=15 | | 9a+4b=7 | | k^2-31-2k=-6-3k^2-2k | | -7(2+7x)=280 | | -2x^2=-2 | | 14-8x=89-43x | | 7a^4-3+2a^9= | | 38.17+X=3X+X | | b^2-9=65 | | 5x^2+9x=-4 | | 3y-8=8y+13 | | 4n^2=64 | | 2x^2-36=x | | 2.1X=20+X | | x^3-4x^2-15x=0 | | 5r^2=80 | | 90-3x=2x+15 | | -6(7+7x)=210 | | 8-9x=77-30x |

Equations solver categories