12x^2+49x-41=0

Simple and best practice solution for 12x^2+49x-41=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 12x^2+49x-41=0 equation: 


Simplifying
12x2 + 49x + -41 = 0

Reorder the terms:
-41 + 49x + 12x2 = 0

Solving
-41 + 49x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-3.416666667 + 4.083333333x + x2 = 0

Move the constant term to the right:

Add '3.416666667' to each side of the equation.
-3.416666667 + 4.083333333x + 3.416666667 + x2 = 0 + 3.416666667

Reorder the terms:
-3.416666667 + 3.416666667 + 4.083333333x + x2 = 0 + 3.416666667

Combine like terms: -3.416666667 + 3.416666667 = 0.000000000
0.000000000 + 4.083333333x + x2 = 0 + 3.416666667
4.083333333x + x2 = 0 + 3.416666667

Combine like terms: 0 + 3.416666667 = 3.416666667
4.083333333x + x2 = 3.416666667

The x term is 4.083333333x.  Take half its coefficient (2.041666667).
Square it (4.168402779) and add it to both sides.

Add '4.168402779' to each side of the equation.
4.083333333x + 4.168402779 + x2 = 3.416666667 + 4.168402779

Reorder the terms:
4.168402779 + 4.083333333x + x2 = 3.416666667 + 4.168402779

Combine like terms: 3.416666667 + 4.168402779 = 7.585069446
4.168402779 + 4.083333333x + x2 = 7.585069446

Factor a perfect square on the left side:
(x + 2.041666667)(x + 2.041666667) = 7.585069446

Calculate the square root of the right side: 2.754100479

Break this problem into two subproblems by setting 
(x + 2.041666667) equal to 2.754100479 and -2.754100479.


Subproblem 1
x + 2.041666667 = 2.754100479

Simplifying
x + 2.041666667 = 2.754100479

Reorder the terms:
2.041666667 + x = 2.754100479

Solving
2.041666667 + x = 2.754100479

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.041666667' to each side of the equation.
2.041666667 + -2.041666667 + x = 2.754100479 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + x = 2.754100479 + -2.041666667
x = 2.754100479 + -2.041666667

Combine like terms: 2.754100479 + -2.041666667 = 0.712433812
x = 0.712433812

Simplifying
x = 0.712433812


Subproblem 2
x + 2.041666667 = -2.754100479

Simplifying
x + 2.041666667 = -2.754100479

Reorder the terms:
2.041666667 + x = -2.754100479

Solving
2.041666667 + x = -2.754100479

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.041666667' to each side of the equation.
2.041666667 + -2.041666667 + x = -2.754100479 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + x = -2.754100479 + -2.041666667
x = -2.754100479 + -2.041666667

Combine like terms: -2.754100479 + -2.041666667 = -4.795767146
x = -4.795767146

Simplifying
x = -4.795767146


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.712433812, -4.795767146}

See similar equations:

| x-0.5x=55000 | | 6(4s+1)=318 | | a^7c^3/a^3 | | 5x+2=3x+(8x+2) | | 0.4=0.2x-1.6 | | 10(2-x)=2x+7-7x+3 | | 6x^2-3=57 | | 2(4y)=12 | | -2/3h=-9 | | -17d+15=27 | | 2(2k+3)+2=11(k-5) | | 6n-5n=3n+10 | | f-4.2=-6 | | 7x-6=21+2x | | -137.76+x=-194.88 | | x^2-3x-162=0 | | 1155/210 | | 3x-17+2x+6=180 | | 4(a+6)-2=-6a+8 | | 5/2y=2/5a | | x^2-3x-162=180 | | -n-2/7=7 | | 5(z-6)-2=9z | | 8(p-1)=4(p+3) | | 2y+a-7y=-6y+2a | | 6x+3x-12=8x-3 | | 1h+20=35-4h | | 3y-a=-3y+a | | 90=-6t | | 12/x=3x | | -3(-2x-5)-7=-10 | | 2(7x+1)=4x-3 |

Equations solver categories