3a^2-24a+32=0

Simple and best practice solution for 3a^2-24a+32=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 3a^2-24a+32=0 equation:


Simplifying
3a2 + -24a + 32 = 0

Reorder the terms:
32 + -24a + 3a2 = 0

Solving
32 + -24a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
10.66666667 + -8a + a2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + -8a + -10.66666667 + a2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + -8a + a2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + -8a + a2 = 0 + -10.66666667
-8a + a2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
-8a + a2 = -10.66666667

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = -10.66666667 + 16

Reorder the terms:
16 + -8a + a2 = -10.66666667 + 16

Combine like terms: -10.66666667 + 16 = 5.33333333
16 + -8a + a2 = 5.33333333

Factor a perfect square on the left side:
(a + -4)(a + -4) = 5.33333333

Calculate the square root of the right side: 2.309401076

Break this problem into two subproblems by setting 
(a + -4) equal to 2.309401076 and -2.309401076.

Subproblem 1

a + -4 = 2.309401076 Simplifying a + -4 = 2.309401076 Reorder the terms: -4 + a = 2.309401076 Solving -4 + a = 2.309401076 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 2.309401076 + 4 Combine like terms: -4 + 4 = 0 0 + a = 2.309401076 + 4 a = 2.309401076 + 4 Combine like terms: 2.309401076 + 4 = 6.309401076 a = 6.309401076 Simplifying a = 6.309401076

Subproblem 2

a + -4 = -2.309401076 Simplifying a + -4 = -2.309401076 Reorder the terms: -4 + a = -2.309401076 Solving -4 + a = -2.309401076 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -2.309401076 + 4 Combine like terms: -4 + 4 = 0 0 + a = -2.309401076 + 4 a = -2.309401076 + 4 Combine like terms: -2.309401076 + 4 = 1.690598924 a = 1.690598924 Simplifying a = 1.690598924

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.309401076, 1.690598924}

See similar equations:

| -5-3=4(x-1) | | 350-4x=0 | | (-3x)-y=6 | | 29.43-0.86x-0.7y=0 | | 350-3.6x=0 | | (0-4)(x+4)=0 | | 11+3x=26 | | 82-7x=0 | | 8x^9/4x^2 | | Y-3=-4(-2-1) | | (x+3)(x-7)=(8x+17)+(7-8x) | | 2a^2-17a+40=0 | | 0.5x-0.7y=0 | | 0.7x-0.7x=0 | | y=.3297x+15.3435 | | (7x-3)(4x-4)=0 | | v/10.44-2.9-4.422 | | -(3w+4)-5(w-2)-3(6w-8)=10 | | g(x)=4x+10 | | 6*x^2+7X-20=0 | | 27/1.8 | | 1.8/27 | | 3x-14-(6-7x)=10 | | (2/5)(3x) | | 3(7h-2)=18 | | y=30x+1400 | | 6(3X+5)-5(8X+6)= | | x-5/6-2(1-x)/3 | | 10m^2+10m=0 | | 27=1.8a | | g(x)=2x^2+3x-1 | | 4x+y-2=6 |

Equations solver categories