4n^2=7n-1

Simple and best practice solution for 4n^2=7n-1 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=7n-1 equation:


Simplifying
4n2 = 7n + -1

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

Solving
4n2 = -1 + 7n

Solving for variable 'n'.

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

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

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

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

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

Divide each side by '4'.
0.25 + -1.75n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.75n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.75n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.75n + n2 = 0 + -0.25
-1.75n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.75n + n2 = -0.25

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 = -0.25 + 0.765625

Reorder the terms:
0.765625 + -1.75n + n2 = -0.25 + 0.765625

Combine like terms: -0.25 + 0.765625 = 0.515625
0.765625 + -1.75n + n2 = 0.515625

Factor a perfect square on the left side:
(n + -0.875)(n + -0.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(n + -0.875) equal to 0.718070331 and -0.718070331.

Subproblem 1

n + -0.875 = 0.718070331 Simplifying n + -0.875 = 0.718070331 Reorder the terms: -0.875 + n = 0.718070331 Solving -0.875 + n = 0.718070331 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 = 0.718070331 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = 0.718070331 + 0.875 n = 0.718070331 + 0.875 Combine like terms: 0.718070331 + 0.875 = 1.593070331 n = 1.593070331 Simplifying n = 1.593070331

Subproblem 2

n + -0.875 = -0.718070331 Simplifying n + -0.875 = -0.718070331 Reorder the terms: -0.875 + n = -0.718070331 Solving -0.875 + n = -0.718070331 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 = -0.718070331 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = -0.718070331 + 0.875 n = -0.718070331 + 0.875 Combine like terms: -0.718070331 + 0.875 = 0.156929669 n = 0.156929669 Simplifying n = 0.156929669

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.593070331, 0.156929669}

See similar equations:

| 4y-28=64 | | (w^3)^7/12 | | 12z+15=168 | | 7x+5(x+3)+4x-x-2+(x+7)= | | (1-w)(2w-9)=0 | | 8w-16=112 | | (n+5)(n+5)=9 | | 8-16=112 | | 6x^2-13x=6 | | c=2m+50 | | 4x+-17=13 | | (x+2)dy+(2x-3y)dy=0 | | 12+6r=180 | | 3W+30=90 | | f(-2)=9-t^2 | | 7*9=(7*10)-(7*b) | | 9/7/-9/5 | | 3+x+8= | | 2/3x=62 | | 3x-62=38+8x | | x+0.75=1 | | K+(-4.2)=-19 | | 12w-7w-4w=8 | | (X-2)dy/dx-y=(x-2)^3 | | 25v^2+36=0 | | 6s+3s-8s-s+3s=12 | | √4/80 | | 4d-3d=17 | | 0=-2+y+5(cos(y))-x^2 | | 8h-5h=6 | | x^3-8x^2+19x-14=y | | -1.5(2x+4+4x)+5x=-.5(1+7x) |

Equations solver categories