6a^2+14a+3=0

Simple and best practice solution for 6a^2+14a+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 6a^2+14a+3=0 equation:


Simplifying
6a2 + 14a + 3 = 0

Reorder the terms:
3 + 14a + 6a2 = 0

Solving
3 + 14a + 6a2 = 0

Solving for variable 'a'.

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

Divide each side by '6'.
0.5 + 2.333333333a + a2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.333333333a + -0.5 + a2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.333333333a + a2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.333333333a + a2 = 0 + -0.5
2.333333333a + a2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.333333333a + a2 = -0.5

The a term is 2.333333333a.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333a + 1.361111112 + a2 = -0.5 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333a + a2 = -0.5 + 1.361111112

Combine like terms: -0.5 + 1.361111112 = 0.861111112
1.361111112 + 2.333333333a + a2 = 0.861111112

Factor a perfect square on the left side:
(a + 1.166666667)(a + 1.166666667) = 0.861111112

Calculate the square root of the right side: 0.927960728

Break this problem into two subproblems by setting 
(a + 1.166666667) equal to 0.927960728 and -0.927960728.

Subproblem 1

a + 1.166666667 = 0.927960728 Simplifying a + 1.166666667 = 0.927960728 Reorder the terms: 1.166666667 + a = 0.927960728 Solving 1.166666667 + a = 0.927960728 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + a = 0.927960728 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + a = 0.927960728 + -1.166666667 a = 0.927960728 + -1.166666667 Combine like terms: 0.927960728 + -1.166666667 = -0.238705939 a = -0.238705939 Simplifying a = -0.238705939

Subproblem 2

a + 1.166666667 = -0.927960728 Simplifying a + 1.166666667 = -0.927960728 Reorder the terms: 1.166666667 + a = -0.927960728 Solving 1.166666667 + a = -0.927960728 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + a = -0.927960728 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + a = -0.927960728 + -1.166666667 a = -0.927960728 + -1.166666667 Combine like terms: -0.927960728 + -1.166666667 = -2.094627395 a = -2.094627395 Simplifying a = -2.094627395

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.238705939, -2.094627395}

See similar equations:

| 10m-870=50 | | -5f+370=-75 | | 2/3x=5.25 | | 16=4x^2-6 | | 6x^2=150x | | -1/3-9 | | M-19=2(4m+1) | | 4(2x+3)+3x=133 | | 72=8p-688 | | 10x-3=3x+2 | | 9c+5c=20 | | -5x-4(2x-3)=-92 | | 6m-11=2/9m-1 | | -1/3*y=12 | | 6(4-x)+6x=2 | | 0=4y^2-23y+33 | | 3(k+1)=18 | | -12.2z-13.4z=-179.2 | | -2r+18=0 | | 110=20-9x | | -7(0.1x+0.2)-1.2=-0.5 | | -15=7r+5r | | 4w-56=20 | | 6x-384/x^20 | | -7x+3(4x+12)=-24 | | (-7)(2/7x)(-3) | | 8x-20=6x+7 | | 2d+60=5d | | 11/20-3/8 | | 9n^2+67n+28=0 | | 3.52+a=8.2 | | 15x=115 |

Equations solver categories