9a^2-64a+36=0

Simple and best practice solution for 9a^2-64a+36=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 9a^2-64a+36=0 equation:


Simplifying
9a2 + -64a + 36 = 0

Reorder the terms:
36 + -64a + 9a2 = 0

Solving
36 + -64a + 9a2 = 0

Solving for variable 'a'.

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

Divide each side by '9'.
4 + -7.111111111a + a2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7.111111111a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + -7.111111111a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7.111111111a + a2 = 0 + -4
-7.111111111a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
-7.111111111a + a2 = -4

The a term is -7.111111111a.  Take half its coefficient (-3.555555556).
Square it (12.64197531) and add it to both sides.

Add '12.64197531' to each side of the equation.
-7.111111111a + 12.64197531 + a2 = -4 + 12.64197531

Reorder the terms:
12.64197531 + -7.111111111a + a2 = -4 + 12.64197531

Combine like terms: -4 + 12.64197531 = 8.64197531
12.64197531 + -7.111111111a + a2 = 8.64197531

Factor a perfect square on the left side:
(a + -3.555555556)(a + -3.555555556) = 8.64197531

Calculate the square root of the right side: 2.939723679

Break this problem into two subproblems by setting 
(a + -3.555555556) equal to 2.939723679 and -2.939723679.

Subproblem 1

a + -3.555555556 = 2.939723679 Simplifying a + -3.555555556 = 2.939723679 Reorder the terms: -3.555555556 + a = 2.939723679 Solving -3.555555556 + a = 2.939723679 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + a = 2.939723679 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + a = 2.939723679 + 3.555555556 a = 2.939723679 + 3.555555556 Combine like terms: 2.939723679 + 3.555555556 = 6.495279235 a = 6.495279235 Simplifying a = 6.495279235

Subproblem 2

a + -3.555555556 = -2.939723679 Simplifying a + -3.555555556 = -2.939723679 Reorder the terms: -3.555555556 + a = -2.939723679 Solving -3.555555556 + a = -2.939723679 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + a = -2.939723679 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + a = -2.939723679 + 3.555555556 a = -2.939723679 + 3.555555556 Combine like terms: -2.939723679 + 3.555555556 = 0.615831877 a = 0.615831877 Simplifying a = 0.615831877

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.495279235, 0.615831877}

See similar equations:

| 9x+3=6x | | 36x=576 | | -7-7x=14 | | 5x+3x+4=180 | | S=-5t^2+22t+15 | | 3x+40+4x+30=180 | | 2x-4-4x-9= | | 12*8=15*x | | log((x^2)+7)=0 | | -4y+3=31 | | log(x^2+7)=0 | | X+(x-10)+(x+40)+x=360 | | 9x+27=2*6x | | -6x+5=-115-9x | | -3(-14)= | | 6x+5=-115-15 | | 2x+43-4x=3-9x+5 | | 7(3x-5)=91 | | (2x+3)+(3x+4)+(5x+5)=12-7x | | 543*34x^2=54x | | -7z=13-8z | | 8x-3-6x=7-3x | | 2(w-3)+7=1-5w | | -22=4x-2(4x-7) | | 4x+6=-3x+4 | | 4x-6=-3x+4 | | 4x+7=-3x-5 | | 4x+7=-3x+5 | | 4x+5=-3x+7 | | x^2+15x+27=4x-1 | | (7-10x)-(8-8x)+(10x+6)=-8 | | x^2+12x+32=5 |

Equations solver categories