4a^2-13a-9=0

Simple and best practice solution for 4a^2-13a-9=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 4a^2-13a-9=0 equation:


Simplifying
4a2 + -13a + -9 = 0

Reorder the terms:
-9 + -13a + 4a2 = 0

Solving
-9 + -13a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-2.25 + -3.25a + a2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -3.25a + 2.25 + a2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -3.25a + a2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -3.25a + a2 = 0 + 2.25
-3.25a + a2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-3.25a + a2 = 2.25

The a term is -3.25a.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25a + 2.640625 + a2 = 2.25 + 2.640625

Reorder the terms:
2.640625 + -3.25a + a2 = 2.25 + 2.640625

Combine like terms: 2.25 + 2.640625 = 4.890625
2.640625 + -3.25a + a2 = 4.890625

Factor a perfect square on the left side:
(a + -1.625)(a + -1.625) = 4.890625

Calculate the square root of the right side: 2.211475752

Break this problem into two subproblems by setting 
(a + -1.625) equal to 2.211475752 and -2.211475752.

Subproblem 1

a + -1.625 = 2.211475752 Simplifying a + -1.625 = 2.211475752 Reorder the terms: -1.625 + a = 2.211475752 Solving -1.625 + a = 2.211475752 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + a = 2.211475752 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + a = 2.211475752 + 1.625 a = 2.211475752 + 1.625 Combine like terms: 2.211475752 + 1.625 = 3.836475752 a = 3.836475752 Simplifying a = 3.836475752

Subproblem 2

a + -1.625 = -2.211475752 Simplifying a + -1.625 = -2.211475752 Reorder the terms: -1.625 + a = -2.211475752 Solving -1.625 + a = -2.211475752 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + a = -2.211475752 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + a = -2.211475752 + 1.625 a = -2.211475752 + 1.625 Combine like terms: -2.211475752 + 1.625 = -0.586475752 a = -0.586475752 Simplifying a = -0.586475752

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.836475752, -0.586475752}

See similar equations:

| 5y=5x+45 | | F(30)=-15 | | 3p-1=2(p-1)-2(7-2p) | | 4km-280m= | | 9-4z=-31+4z | | 6x^4+34x^3+20p^2=0 | | -6-6x=-7x+2 | | 3x^2-5x-1= | | 2.07*9.1= | | 96.1+1.10x=83.7+2.70x | | 8r^2+6r-5=0 | | 5x+8-2x-12=7x+16 | | 330=-5u | | 1x-2y=12 | | 18.95+7.05= | | (2x+20)(2x+15)=1400 | | 21x-7y=84 | | 1-x=3x-1 | | -5(16.5+2t)=3(0.9-t) | | 4y-5x(11+4y)=9 | | 3.3*0.75= | | 4/55= | | x^2+1=3x^2+13 | | 55/4= | | y=5x^2+8x+21 | | -3(x+10)+2x=75 | | 1x-2y+4=2 | | 2=92-9x | | 12x^2-24x-96=0 | | 3x-5+2x^2+9x=3x+2x^2+9x-5 | | 9b^4-3b-6b^3+2=0 | | 177258+32.90x=73272+610.60x |

Equations solver categories