7n^2-6n-7=0

Simple and best practice solution for 7n^2-6n-7=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 7n^2-6n-7=0 equation:


Simplifying
7n2 + -6n + -7 = 0

Reorder the terms:
-7 + -6n + 7n2 = 0

Solving
-7 + -6n + 7n2 = 0

Solving for variable 'n'.

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

Divide each side by '7'.
-1 + -0.8571428571n + n2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.8571428571n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.8571428571n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.8571428571n + n2 = 0 + 1
-0.8571428571n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.8571428571n + n2 = 1

The n term is -0.8571428571n.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571n + 0.1836734694 + n2 = 1 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571n + n2 = 1 + 0.1836734694

Combine like terms: 1 + 0.1836734694 = 1.1836734694
0.1836734694 + -0.8571428571n + n2 = 1.1836734694

Factor a perfect square on the left side:
(n + -0.4285714286)(n + -0.4285714286) = 1.1836734694

Calculate the square root of the right side: 1.087967587

Break this problem into two subproblems by setting 
(n + -0.4285714286) equal to 1.087967587 and -1.087967587.

Subproblem 1

n + -0.4285714286 = 1.087967587 Simplifying n + -0.4285714286 = 1.087967587 Reorder the terms: -0.4285714286 + n = 1.087967587 Solving -0.4285714286 + n = 1.087967587 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + n = 1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + n = 1.087967587 + 0.4285714286 n = 1.087967587 + 0.4285714286 Combine like terms: 1.087967587 + 0.4285714286 = 1.5165390156 n = 1.5165390156 Simplifying n = 1.5165390156

Subproblem 2

n + -0.4285714286 = -1.087967587 Simplifying n + -0.4285714286 = -1.087967587 Reorder the terms: -0.4285714286 + n = -1.087967587 Solving -0.4285714286 + n = -1.087967587 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + n = -1.087967587 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + n = -1.087967587 + 0.4285714286 n = -1.087967587 + 0.4285714286 Combine like terms: -1.087967587 + 0.4285714286 = -0.6593961584 n = -0.6593961584 Simplifying n = -0.6593961584

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.5165390156, -0.6593961584}

See similar equations:

| 0.62x+110=0.12x+130 | | 5n-11=2xn+4 | | x^-35/x^-30 | | 3e+2e+5e= | | 5x+20y=500 | | 3*x-5=x+19 | | (4x-3)*2+(5x+7)=8x | | 8-5x=5x-2 | | 90=(x+8)+2x | | 5+3=15 | | -3x+7=-4x-64 | | -3=1/3s | | 2(f-8)=-10 | | -6g+36=13 | | 7(9x+5)-8= | | -10(s+4)=-53 | | -8x+3+8x=-9-4x+8 | | 3b^2+10b-13=0 | | 5y/(7y-8) | | 3y+5=19 | | -4+3(x-1)=2(x+2)-x | | 216=w(w-6) | | 3x-21/6-x | | 3x^36/x^71 | | 16x^4+13x^2-3=0 | | -59.75/12 | | (x+1)+(x+1)+(x-2)=180 | | -4(-8-9x)= | | e^3=.5x-1 | | 2n^2+6n-9=0 | | 4(3s+4)=136 | | 4x+5=3x+27 |

Equations solver categories