12a^2+9a-13=0

Simple and best practice solution for 12a^2+9a-13=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+9a-13=0 equation:


Simplifying
12a2 + 9a + -13 = 0

Reorder the terms:
-13 + 9a + 12a2 = 0

Solving
-13 + 9a + 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'.
-1.083333333 + 0.75a + a2 = 0

Move the constant term to the right:

Add '1.083333333' to each side of the equation.
-1.083333333 + 0.75a + 1.083333333 + a2 = 0 + 1.083333333

Reorder the terms:
-1.083333333 + 1.083333333 + 0.75a + a2 = 0 + 1.083333333

Combine like terms: -1.083333333 + 1.083333333 = 0.000000000
0.000000000 + 0.75a + a2 = 0 + 1.083333333
0.75a + a2 = 0 + 1.083333333

Combine like terms: 0 + 1.083333333 = 1.083333333
0.75a + a2 = 1.083333333

The a term is 0.75a.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75a + 0.140625 + a2 = 1.083333333 + 0.140625

Reorder the terms:
0.140625 + 0.75a + a2 = 1.083333333 + 0.140625

Combine like terms: 1.083333333 + 0.140625 = 1.223958333
0.140625 + 0.75a + a2 = 1.223958333

Factor a perfect square on the left side:
(a + 0.375)(a + 0.375) = 1.223958333

Calculate the square root of the right side: 1.106326504

Break this problem into two subproblems by setting 
(a + 0.375) equal to 1.106326504 and -1.106326504.

Subproblem 1

a + 0.375 = 1.106326504 Simplifying a + 0.375 = 1.106326504 Reorder the terms: 0.375 + a = 1.106326504 Solving 0.375 + a = 1.106326504 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + a = 1.106326504 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + a = 1.106326504 + -0.375 a = 1.106326504 + -0.375 Combine like terms: 1.106326504 + -0.375 = 0.731326504 a = 0.731326504 Simplifying a = 0.731326504

Subproblem 2

a + 0.375 = -1.106326504 Simplifying a + 0.375 = -1.106326504 Reorder the terms: 0.375 + a = -1.106326504 Solving 0.375 + a = -1.106326504 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + a = -1.106326504 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + a = -1.106326504 + -0.375 a = -1.106326504 + -0.375 Combine like terms: -1.106326504 + -0.375 = -1.481326504 a = -1.481326504 Simplifying a = -1.481326504

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.731326504, -1.481326504}

See similar equations:

| 2y-(3*0.6y+2.7)= | | 24a-18b= | | Z*7-6=2 | | -7(x+2)-4=12x+5 | | 4(x-6)=3(2+x) | | P^2-7p+7=0 | | -3/2x-2=6/4x-3 | | 9x^2+24-16=0 | | 8(x+8)-(4+4x)=3x | | F(x)=6x^2-3x-3 | | (4x-8)/x=12 | | 0=27x^3-1 | | (4x-8/x)=12 | | 8x^5+4x^2-12= | | 268+w=687 | | 4(4+y)= | | 2(x-4)/x=12 | | -2(n-7)=4-4 | | 10h+2=75 | | 5.7=17.3 | | 12x+6y=1080 | | 1x+2y+1z=0 | | t*5-5=9 | | 3x-9=6x-1 | | 5x^2+5-13x=0 | | 7(2y-1)+3y=-3(y+2)15 | | -12x^4y-9x^3y^2+3x^2y^3=0 | | 10a=-50 | | Xdy/dx=3^y/xy | | x=7+6 | | Csc^4x-1=0 | | 4y-x=-60 |

Equations solver categories