7n^2+488n-5=7n+1

Simple and best practice solution for 7n^2+488n-5=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 7n^2+488n-5=7n+1 equation:


Simplifying
7n2 + 488n + -5 = 7n + 1

Reorder the terms:
-5 + 488n + 7n2 = 7n + 1

Reorder the terms:
-5 + 488n + 7n2 = 1 + 7n

Solving
-5 + 488n + 7n2 = 1 + 7n

Solving for variable 'n'.

Reorder the terms:
-5 + -1 + 488n + -7n + 7n2 = 1 + 7n + -1 + -7n

Combine like terms: -5 + -1 = -6
-6 + 488n + -7n + 7n2 = 1 + 7n + -1 + -7n

Combine like terms: 488n + -7n = 481n
-6 + 481n + 7n2 = 1 + 7n + -1 + -7n

Reorder the terms:
-6 + 481n + 7n2 = 1 + -1 + 7n + -7n

Combine like terms: 1 + -1 = 0
-6 + 481n + 7n2 = 0 + 7n + -7n
-6 + 481n + 7n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-6 + 481n + 7n2 = 0

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

Divide each side by '7'.
-0.8571428571 + 68.71428571n + n2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + 68.71428571n + 0.8571428571 + n2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + 68.71428571n + n2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + 68.71428571n + n2 = 0 + 0.8571428571
68.71428571n + n2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
68.71428571n + n2 = 0.8571428571

The n term is 68.71428571n.  Take half its coefficient (34.35714286).
Square it (1180.413266) and add it to both sides.

Add '1180.413266' to each side of the equation.
68.71428571n + 1180.413266 + n2 = 0.8571428571 + 1180.413266

Reorder the terms:
1180.413266 + 68.71428571n + n2 = 0.8571428571 + 1180.413266

Combine like terms: 0.8571428571 + 1180.413266 = 1181.2704088571
1180.413266 + 68.71428571n + n2 = 1181.2704088571

Factor a perfect square on the left side:
(n + 34.35714286)(n + 34.35714286) = 1181.2704088571

Calculate the square root of the right side: 34.369614616

Break this problem into two subproblems by setting 
(n + 34.35714286) equal to 34.369614616 and -34.369614616.

Subproblem 1

n + 34.35714286 = 34.369614616 Simplifying n + 34.35714286 = 34.369614616 Reorder the terms: 34.35714286 + n = 34.369614616 Solving 34.35714286 + n = 34.369614616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-34.35714286' to each side of the equation. 34.35714286 + -34.35714286 + n = 34.369614616 + -34.35714286 Combine like terms: 34.35714286 + -34.35714286 = 0.00000000 0.00000000 + n = 34.369614616 + -34.35714286 n = 34.369614616 + -34.35714286 Combine like terms: 34.369614616 + -34.35714286 = 0.012471756 n = 0.012471756 Simplifying n = 0.012471756

Subproblem 2

n + 34.35714286 = -34.369614616 Simplifying n + 34.35714286 = -34.369614616 Reorder the terms: 34.35714286 + n = -34.369614616 Solving 34.35714286 + n = -34.369614616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-34.35714286' to each side of the equation. 34.35714286 + -34.35714286 + n = -34.369614616 + -34.35714286 Combine like terms: 34.35714286 + -34.35714286 = 0.00000000 0.00000000 + n = -34.369614616 + -34.35714286 n = -34.369614616 + -34.35714286 Combine like terms: -34.369614616 + -34.35714286 = -68.726757476 n = -68.726757476 Simplifying n = -68.726757476

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.012471756, -68.726757476}

See similar equations:

| 4n-40=7(-2n+n) | | 7x+32=4y | | 16x+36=14x+50 | | 10n^2+15n+8=3n^2 | | 10=2/3+7 | | -80=8(-6+n) | | 2x+46= | | -6x-22=8 | | 10=2/z+7 | | (1/4)x^3-3x=0 | | 3xsquared=6 | | 8=3w+5w | | -b^2-2b=0 | | 3(-7+48(3)+6(3)(7)+7(3)2+8(3)2(7)+(3)2(7)2)= | | 5x-10(x-2)=6 | | 8d+3=19 | | 8. 3(-7+48(3)+6(3)(7)+7(3)2+8(3)2(7)+(3)2(7)2)= | | 9w+43=-2(w+6) | | 2.6a+4.5b-8.2a-(-4.5b)= | | M^2+2m-29=-5 | | 2(w-4)=9w-43 | | 3(x-1)=9-(x-1) | | 2u+28=-9(u-8) | | X^2+15x+61=5 | | 15-2/3 | | -7+144+126+42+336+84= | | -19=4(y+2)-7y | | x+3z+y+4y+x+4= | | 2w+7(w-4)=26 | | 4y-20=44 | | 10=-6/2+7 | | 28=8(x+3)-4x |

Equations solver categories