7n+58-n^2=4

Simple and best practice solution for 7n+58-n^2=4 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 7n+58-n^2=4 equation:


Simplifying
7n + 58 + -1n2 = 4

Reorder the terms:
58 + 7n + -1n2 = 4

Solving
58 + 7n + -1n2 = 4

Solving for variable 'n'.

Reorder the terms:
58 + -4 + 7n + -1n2 = 4 + -4

Combine like terms: 58 + -4 = 54
54 + 7n + -1n2 = 4 + -4

Combine like terms: 4 + -4 = 0
54 + 7n + -1n2 = 0

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

Divide each side by '-1'.
-54 + -7n + n2 = 0

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -7n + 54 + n2 = 0 + 54

Reorder the terms:
-54 + 54 + -7n + n2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -7n + n2 = 0 + 54
-7n + n2 = 0 + 54

Combine like terms: 0 + 54 = 54
-7n + n2 = 54

The n term is -7n.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7n + 12.25 + n2 = 54 + 12.25

Reorder the terms:
12.25 + -7n + n2 = 54 + 12.25

Combine like terms: 54 + 12.25 = 66.25
12.25 + -7n + n2 = 66.25

Factor a perfect square on the left side:
(n + -3.5)(n + -3.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(n + -3.5) equal to 8.139410298 and -8.139410298.

Subproblem 1

n + -3.5 = 8.139410298 Simplifying n + -3.5 = 8.139410298 Reorder the terms: -3.5 + n = 8.139410298 Solving -3.5 + n = 8.139410298 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = 8.139410298 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = 8.139410298 + 3.5 n = 8.139410298 + 3.5 Combine like terms: 8.139410298 + 3.5 = 11.639410298 n = 11.639410298 Simplifying n = 11.639410298

Subproblem 2

n + -3.5 = -8.139410298 Simplifying n + -3.5 = -8.139410298 Reorder the terms: -3.5 + n = -8.139410298 Solving -3.5 + n = -8.139410298 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = -8.139410298 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = -8.139410298 + 3.5 n = -8.139410298 + 3.5 Combine like terms: -8.139410298 + 3.5 = -4.639410298 n = -4.639410298 Simplifying n = -4.639410298

Solution

The solution to the problem is based on the solutions from the subproblems. n = {11.639410298, -4.639410298}

See similar equations:

| 4x/16=20/4 | | 5/2=4?x | | 9/x=12/21 | | 5x^2-15=49 | | 14x=104 | | 1/3b8 | | 86=215-x | | 2cost=0 | | 210-v=119 | | Ln(3x)+2=7 | | (y+2)i=2yi | | 2z-16=-51+9z | | 6y+12=7y-6 | | (6)3/4 | | log^5(4x-9)=2 | | 2z-26=-44+8z | | 2yi=2yi | | 4(5X)=16 | | 4X(5x)=16 | | y=-2.9x+3.8 | | 1/2y-1/5=-2/3 | | 180/2=2x | | 8x+32=21x+33 | | 3x^2-5x-1-8x^2+2x-9= | | (3+2x)(3x-2)=0 | | a^2+7ab+12b=0 | | (4x+3)(x-5)=16x+12 | | 3x=3x^2-6x | | 1.4(x)+6.1=-7.9 | | 3m=2m | | x*w=-32 | | 358b-(49b)*75= |

Equations solver categories