3x^2-2ax-2a^2=0

Simple and best practice solution for 3x^2-2ax-2a^2=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 3x^2-2ax-2a^2=0 equation: 


Simplifying
3x2 + -2ax + -2a2 = 0

Reorder the terms:
-2ax + -2a2 + 3x2 = 0

Solving
-2ax + -2a2 + 3x2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
ax + a2 + -1.5x2 = 0

Move the constant term to the right:

Add '1.5x2' to each side of the equation.
ax + a2 + -1.5x2 + 1.5x2 = 0 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
ax + a2 + 0.0 = 0 + 1.5x2
ax + a2 = 0 + 1.5x2
Remove the zero:
ax + a2 = 1.5x2

The a term is ax.  Take half its coefficient (0.5x).
Square it (0.25x2) and add it to both sides.

Add '0.25x2' to each side of the equation.
x2 + a2 + 0.25x2 = 1.5x2 + 0.25x2

Reorder the terms:
a2 + x2 + 0.25x2 = 1.5x2 + 0.25x2

Combine like terms: x2 + 0.25x2 = 1.25x2
a2 + 1.25x2 = 1.5x2 + 0.25x2

Combine like terms: 1.5x2 + 0.25x2 = 1.75x2
a2 + 1.25x2 = 1.75x2

Factor a perfect square on the left side:
(a + 0.5x)(a + 0.5x) = 1.75x2

Calculate the square root of the right side: 1.322875656x

Break this problem into two subproblems by setting 
(a + 0.5x) equal to 1.322875656x and -1.322875656x.


Subproblem 1
a + 0.5x = 1.322875656x

Simplifying
a + 0.5x = 1.322875656x

Solving
a + 0.5x = 1.322875656x

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.5x' to each side of the equation.
a + 0.5x + -0.5x = 1.322875656x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
a + 0.0 = 1.322875656x + -0.5x
a = 1.322875656x + -0.5x

Combine like terms: 1.322875656x + -0.5x = 0.822875656x
a = 0.822875656x

Simplifying
a = 0.822875656x


Subproblem 2
a + 0.5x = -1.322875656x

Simplifying
a + 0.5x = -1.322875656x

Solving
a + 0.5x = -1.322875656x

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.5x' to each side of the equation.
a + 0.5x + -0.5x = -1.322875656x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
a + 0.0 = -1.322875656x + -0.5x
a = -1.322875656x + -0.5x

Combine like terms: -1.322875656x + -0.5x = -1.822875656x
a = -1.822875656x

Simplifying
a = -1.822875656x


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.822875656x, -1.822875656x}

See similar equations:

| 3x=9x+8 | | 7x-14=10x+10 | | (x+4)squared=x(x+12) | | (x+4)2=x(x+12) | | 4(1-y)+3y=1 | | 5x^2/5x^2 | | X+x+200=205-200 | | (4x^2)-24x+45=0 | | x+x+200=205-x | | 9y+10x-6xy=8 | | 2x+2x+12=180 | | x+x+200=205 | | 10/18=x/3 | | 5(13+3)=210 | | Y=x+200 | | 6y-13=-21-28 | | 3x-2m^2=3 | | X+(x-200)=205 | | 38+6x-5x=2x+7 | | 0.34x=15 | | 2y^2+y^2=20 | | 5v+-8v=-3v | | (a+2)(a+2)=60+3a | | (a+2)x(a+2)=60+3a | | 10x-12=6x+16 | | (a+2)(a+2)=60-3a | | 5w+3y= | | (a+2)x(a+2)=60-3a | | 5x-3x+15=35 | | (3-4j)(3j-2)/-j | | 18x=-26x | | 7b=-3.5 |

Equations solver categories