12a^2+6a-5=0

Simple and best practice solution for 12a^2+6a-5=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 12a^2+6a-5=0 equation:


Simplifying
12a2 + 6a + -5 = 0

Reorder the terms:
-5 + 6a + 12a2 = 0

Solving
-5 + 6a + 12a2 = 0

Solving for variable 'a'.

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

Divide each side by '12'.
-0.4166666667 + 0.5a + a2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.5a + 0.4166666667 + a2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 0.5a + a2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 0.5a + a2 = 0 + 0.4166666667
0.5a + a2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
0.5a + a2 = 0.4166666667

The a term is 0.5a.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5a + 0.0625 + a2 = 0.4166666667 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = 0.4166666667 + 0.0625

Combine like terms: 0.4166666667 + 0.0625 = 0.4791666667
0.0625 + 0.5a + a2 = 0.4791666667

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = 0.4791666667

Calculate the square root of the right side: 0.692218655

Break this problem into two subproblems by setting 
(a + 0.25) equal to 0.692218655 and -0.692218655.

Subproblem 1

a + 0.25 = 0.692218655 Simplifying a + 0.25 = 0.692218655 Reorder the terms: 0.25 + a = 0.692218655 Solving 0.25 + a = 0.692218655 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + a = 0.692218655 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + a = 0.692218655 + -0.25 a = 0.692218655 + -0.25 Combine like terms: 0.692218655 + -0.25 = 0.442218655 a = 0.442218655 Simplifying a = 0.442218655

Subproblem 2

a + 0.25 = -0.692218655 Simplifying a + 0.25 = -0.692218655 Reorder the terms: 0.25 + a = -0.692218655 Solving 0.25 + a = -0.692218655 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + a = -0.692218655 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + a = -0.692218655 + -0.25 a = -0.692218655 + -0.25 Combine like terms: -0.692218655 + -0.25 = -0.942218655 a = -0.942218655 Simplifying a = -0.942218655

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.442218655, -0.942218655}

See similar equations:

| 2+2*2=2 | | (y-12)(6x-32)(3y-8)(2x-20)= | | 5x-(3x-7)= | | 8c^2+22cd+9d^2=0 | | 105x^4+60x^3-30x^6= | | 6*x^4-2*x^2=n | | -13a+6-9a+12a= | | 6c^2+7cd-5d^2=0 | | (75)(5x-2)= | | 2a^2-11ab-6b^2=0 | | 3a^2+ab-10b^2=0 | | 6x^2*x^2=n | | 6+2(7+x)+8y=36+2y+10x | | 3x-1+2x^2=n | | 6x(-2x+1)=-11(x+1) | | F(-3)=x^4+3x^2+5 | | (11b-4)-5(2b+2)=-4 | | 6+2(7+x)=36+2y+10x | | 3=7y-5y-3 | | 4x+5y=-13 | | 14=-15x+4x | | 8x+6x+4+9=5x+5+8x | | 14=15x+4x | | 8=6y-4y | | 5x+11x=64 | | 3-x-7=3(x+1) | | n+5-5=12-5 | | 3-(5)-7=3((-5)+1) | | 3x^2-7+2=0 | | x+4(x-6)= | | 2(3x+2)=26 | | 4(-4)+8(-2)+3(-2)+6= |

Equations solver categories