a^2-a+4a-3a^2+1=0

Simple and best practice solution for a^2-a+4a-3a^2+1=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 a^2-a+4a-3a^2+1=0 equation:


Simplifying
a2 + -1a + 4a + -3a2 + 1 = 0

Reorder the terms:
1 + -1a + 4a + a2 + -3a2 = 0

Combine like terms: -1a + 4a = 3a
1 + 3a + a2 + -3a2 = 0

Combine like terms: a2 + -3a2 = -2a2
1 + 3a + -2a2 = 0

Solving
1 + 3a + -2a2 = 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'.
-0.5 + -1.5a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.5a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.5a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.5a + a2 = 0 + 0.5
-1.5a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.5a + a2 = 0.5

The a term is -1.5a.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5a + 0.5625 + a2 = 0.5 + 0.5625

Reorder the terms:
0.5625 + -1.5a + a2 = 0.5 + 0.5625

Combine like terms: 0.5 + 0.5625 = 1.0625
0.5625 + -1.5a + a2 = 1.0625

Factor a perfect square on the left side:
(a + -0.75)(a + -0.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(a + -0.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

a + -0.75 = 1.030776406 Simplifying a + -0.75 = 1.030776406 Reorder the terms: -0.75 + a = 1.030776406 Solving -0.75 + a = 1.030776406 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 1.030776406 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 1.030776406 + 0.75 a = 1.030776406 + 0.75 Combine like terms: 1.030776406 + 0.75 = 1.780776406 a = 1.780776406 Simplifying a = 1.780776406

Subproblem 2

a + -0.75 = -1.030776406 Simplifying a + -0.75 = -1.030776406 Reorder the terms: -0.75 + a = -1.030776406 Solving -0.75 + a = -1.030776406 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -1.030776406 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -1.030776406 + 0.75 a = -1.030776406 + 0.75 Combine like terms: -1.030776406 + 0.75 = -0.280776406 a = -0.280776406 Simplifying a = -0.280776406

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.780776406, -0.280776406}

See similar equations:

| 62=2-6k | | |5n+1|=11 | | 4m=a | | 7a=.49 | | 17=-x-3-3x | | 9r^2=-1 | | 0=3(8+b) | | 4a^2=7a+92 | | |4t|=20 | | 4+m-t=2 | | x+39+56=x+31 | | 7(x-5)-4=-3(-8x+7)-5x | | 10-4c=4+2x | | -7-9p=56 | | 5x-23=76 | | lny=3x+2 | | 2(2x-1)=20 | | x-1+4=3x-1 | | 2t-40+t+60=900 | | -(3h-15)=6(2h+5) | | 3x-5=9x+25 | | 0.3x+0.7(x-0.1)=12.82 | | -1-5=-20 | | 49y^2+16w^2-56yw=0 | | 10x^2-11x-1=0 | | X^2+13x+25=6x+43 | | 0=4(x+1)-21-7(x-2) | | k(x)=ln(x-3) | | 6[5p+4]-16=20 | | [(x^4)-(6x^3)+(8x^2)+16x-64]=0 | | 7x=2(x-15) | | 295+39e=350+33e |

Equations solver categories