12x^2+14x+3=0

Simple and best practice solution for 12x^2+14x+3=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+14x+3=0 equation:


Simplifying
12x2 + 14x + 3 = 0

Reorder the terms:
3 + 14x + 12x2 = 0

Solving
3 + 14x + 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'.
0.25 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 1.166666667x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 1.166666667x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 1.166666667x + x2 = 0 + -0.25
1.166666667x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
1.166666667x + x2 = -0.25

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = -0.25 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = -0.25 + 0.3402777780

Combine like terms: -0.25 + 0.3402777780 = 0.090277778
0.3402777780 + 1.166666667x + x2 = 0.090277778

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = 0.090277778

Calculate the square root of the right side: 0.300462607

Break this problem into two subproblems by setting 
(x + 0.5833333335) equal to 0.300462607 and -0.300462607.

Subproblem 1

x + 0.5833333335 = 0.300462607 Simplifying x + 0.5833333335 = 0.300462607 Reorder the terms: 0.5833333335 + x = 0.300462607 Solving 0.5833333335 + x = 0.300462607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 0.300462607 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.300462607 + -0.5833333335 x = 0.300462607 + -0.5833333335 Combine like terms: 0.300462607 + -0.5833333335 = -0.2828707265 x = -0.2828707265 Simplifying x = -0.2828707265

Subproblem 2

x + 0.5833333335 = -0.300462607 Simplifying x + 0.5833333335 = -0.300462607 Reorder the terms: 0.5833333335 + x = -0.300462607 Solving 0.5833333335 + x = -0.300462607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -0.300462607 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.300462607 + -0.5833333335 x = -0.300462607 + -0.5833333335 Combine like terms: -0.300462607 + -0.5833333335 = -0.8837959405 x = -0.8837959405 Simplifying x = -0.8837959405

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.2828707265, -0.8837959405}

See similar equations:

| 7(14)=6(x-3) | | 37-(2g+3)=4(g+5)+g | | -9=y/(-3-6) | | -6c=2+3 | | -6c=2+3 | | -6c=2+3 | | 1/2=(1/2)t+3 | | 9(x-1)-2=5(x-3)-(-4x-7) | | 26x-2=18x+48x | | 3m(8-m)= | | 4y^2+2y(3y-2)-3y^2=0 | | 4/5-8=4 | | 30w+10=40+29w | | 2*10+y=19 | | 10-5+3+r= | | 6w+45=3(w+5) | | 4x=4(3) | | -3(-5h-4)=2(10h+8) | | 3.2/x=2.75/0.4 | | 1.5(x+7)=20 | | -8x+1-4+7+x-4= | | 0.3+2.4=0.1+4 | | 2x^2+19x-6=180 | | H/-11=21 | | 1.67(110.3)=1x | | 6t-5t+12=16 | | 48+8y=96 | | z/6+1=7-z/6 | | R=r^1+r^2 | | 495=.80x+7 | | 285=20s+60 | | -1+10x=20 |

Equations solver categories