8n^2=38n-10

Simple and best practice solution for 8n^2=38n-10 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 8n^2=38n-10 equation:


Simplifying
8n2 = 38n + -10

Reorder the terms:
8n2 = -10 + 38n

Solving
8n2 = -10 + 38n

Solving for variable 'n'.

Reorder the terms:
10 + -38n + 8n2 = -10 + 38n + 10 + -38n

Reorder the terms:
10 + -38n + 8n2 = -10 + 10 + 38n + -38n

Combine like terms: -10 + 10 = 0
10 + -38n + 8n2 = 0 + 38n + -38n
10 + -38n + 8n2 = 38n + -38n

Combine like terms: 38n + -38n = 0
10 + -38n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -19n + 4n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -19n + 4n2)' equal to zero and attempt to solve: Simplifying 5 + -19n + 4n2 = 0 Solving 5 + -19n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -4.75n + n2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4.75n + -1.25 + n2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4.75n + n2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4.75n + n2 = 0 + -1.25 -4.75n + n2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4.75n + n2 = -1.25 The n term is -4.75n. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75n + 5.640625 + n2 = -1.25 + 5.640625 Reorder the terms: 5.640625 + -4.75n + n2 = -1.25 + 5.640625 Combine like terms: -1.25 + 5.640625 = 4.390625 5.640625 + -4.75n + n2 = 4.390625 Factor a perfect square on the left side: (n + -2.375)(n + -2.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (n + -2.375) equal to 2.095381827 and -2.095381827.

Subproblem 1

n + -2.375 = 2.095381827 Simplifying n + -2.375 = 2.095381827 Reorder the terms: -2.375 + n = 2.095381827 Solving -2.375 + n = 2.095381827 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + n = 2.095381827 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + n = 2.095381827 + 2.375 n = 2.095381827 + 2.375 Combine like terms: 2.095381827 + 2.375 = 4.470381827 n = 4.470381827 Simplifying n = 4.470381827

Subproblem 2

n + -2.375 = -2.095381827 Simplifying n + -2.375 = -2.095381827 Reorder the terms: -2.375 + n = -2.095381827 Solving -2.375 + n = -2.095381827 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + n = -2.095381827 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + n = -2.095381827 + 2.375 n = -2.095381827 + 2.375 Combine like terms: -2.095381827 + 2.375 = 0.279618173 n = 0.279618173 Simplifying n = 0.279618173

Solution

The solution to the problem is based on the solutions from the subproblems. n = {4.470381827, 0.279618173}

Solution

n = {4.470381827, 0.279618173}

See similar equations:

| 6x(4-3)+49= | | -11.2-z=28.3 | | 4n^2+19n-5=0 | | 8-7p=3 | | 6/7z=12 | | 5+3t=6 | | -2w+9=15 | | 4-5z=54 | | x+0y=7 | | 8k+2=18 | | x^4-25(x^2)+144=0 | | -54=9c | | 1/4m=1/2 | | n^2-4n-12=30 | | 1/2x+1/3x+1/8x+1 | | 8+3x=x-4(4+x) | | 2x-5+3x+1=3x-2 | | 4x-20=4+4x | | y*y^2-2yz-15z^2=0 | | (y)y^2-2yz-15z^2=0 | | 0.03x^3+0.05x^2-3=0 | | 4x+2x=9x+14 | | 34-6x+109-21x+81-12x=180 | | -1+3k=-11-2k+3k | | 8+7a=a+2 | | 4(2y-1)=10(y+5) | | 2(x+4)+2(x+5)=18 | | 4x-2=x+8 | | 12=--4(-6x-3) | | -15-6r-5+8=-8r+4r | | -15-6r-5+8=8r+4r | | (4x+38)=(7x+5) |

Equations solver categories