n^2-15n-37=0

Simple and best practice solution for n^2-15n-37=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^2-15n-37=0 equation:


Simplifying
n2 + -15n + -37 = 0

Reorder the terms:
-37 + -15n + n2 = 0

Solving
-37 + -15n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -15n + 37 + n2 = 0 + 37

Reorder the terms:
-37 + 37 + -15n + n2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -15n + n2 = 0 + 37
-15n + n2 = 0 + 37

Combine like terms: 0 + 37 = 37
-15n + n2 = 37

The n term is -15n.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15n + 56.25 + n2 = 37 + 56.25

Reorder the terms:
56.25 + -15n + n2 = 37 + 56.25

Combine like terms: 37 + 56.25 = 93.25
56.25 + -15n + n2 = 93.25

Factor a perfect square on the left side:
(n + -7.5)(n + -7.5) = 93.25

Calculate the square root of the right side: 9.656603958

Break this problem into two subproblems by setting 
(n + -7.5) equal to 9.656603958 and -9.656603958.

Subproblem 1

n + -7.5 = 9.656603958 Simplifying n + -7.5 = 9.656603958 Reorder the terms: -7.5 + n = 9.656603958 Solving -7.5 + n = 9.656603958 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = 9.656603958 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 9.656603958 + 7.5 n = 9.656603958 + 7.5 Combine like terms: 9.656603958 + 7.5 = 17.156603958 n = 17.156603958 Simplifying n = 17.156603958

Subproblem 2

n + -7.5 = -9.656603958 Simplifying n + -7.5 = -9.656603958 Reorder the terms: -7.5 + n = -9.656603958 Solving -7.5 + n = -9.656603958 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = -9.656603958 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -9.656603958 + 7.5 n = -9.656603958 + 7.5 Combine like terms: -9.656603958 + 7.5 = -2.156603958 n = -2.156603958 Simplifying n = -2.156603958

Solution

The solution to the problem is based on the solutions from the subproblems. n = {17.156603958, -2.156603958}

See similar equations:

| 7g-5g=14 | | -3r-8+7t=34+9t-2 | | 2(x-7)+9x=-3 | | 2y-18x=-16 | | -11n-12+9n=18 | | 5x^2=2x-8 | | 400x=200x+442857.14 | | 2x-5=-35 | | 6x-8y=5 | | 5q-3b+6q-5q+8b= | | 16v-7v-4v+2v=14 | | -2(4.36-6.92x)=9.72x+3.87 | | -4-6+15-6=39 | | 0=2x^2-10x+8 | | 12=5x+3x+4 | | 24n-40=20n-4 | | 20v-6v-11v-3v+v=20 | | 11m=132 | | 7x-10=4x+16 | | 45=x+16 | | 3x-8m+3m-6x= | | 6-z=-1 | | 2.50(x+15)=x | | 7500.00+150.00x=0 | | 17z-10z+z-6z=18 | | 6.1X-4=5.1X | | 0=-16x^2+60 | | 2(4+x)=10-3x | | x=500+60 | | 7x-10=4x-16 | | 2p-7(4p+4)=-28 | | 50=34-4(x-2) |

Equations solver categories