a^2-3a+1=0

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


Simplifying
a2 + -3a + 1 = 0

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

Solving
1 + -3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3a + -1 + a2 = 0 + -1

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

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

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

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -1 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3a + a2 = 1.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

a + -1.5 = 1.118033989 Simplifying a + -1.5 = 1.118033989 Reorder the terms: -1.5 + a = 1.118033989 Solving -1.5 + a = 1.118033989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 1.118033989 + 1.5 a = 1.118033989 + 1.5 Combine like terms: 1.118033989 + 1.5 = 2.618033989 a = 2.618033989 Simplifying a = 2.618033989

Subproblem 2

a + -1.5 = -1.118033989 Simplifying a + -1.5 = -1.118033989 Reorder the terms: -1.5 + a = -1.118033989 Solving -1.5 + a = -1.118033989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -1.118033989 + 1.5 a = -1.118033989 + 1.5 Combine like terms: -1.118033989 + 1.5 = 0.381966011 a = 0.381966011 Simplifying a = 0.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.618033989, 0.381966011}

See similar equations:

| 4x-7=x-2 | | ln(x+1)=5 | | 5y+3x=3 | | -5+8x=5x-14 | | z(z+2)=(z*z)+2z+1 | | 9x-6=129 | | -7(x+4)=3x+2 | | 5x^2+8x-21=0 | | 4x^2+22x+24=0 | | 6p-31=47 | | 2n+36-n=4n+(2*3)-6+n | | 4x^2-42=5x^2+17x | | 4x-25=7-4x | | 2n+36-n=4n+(2+3)-6+n | | x^2-4xy+100=0 | | 2-(5s+7)=7+s | | 8(a+2)=9a | | 9y-8=y | | 21q+-11=10 | | 18w-2=10w+4 | | 5d+-9=-24 | | x^2+7x+3.5=0 | | x^2-11x+4=0 | | -3x(7x-4)+6x-(13-24x^2)= | | 3x^2*2x-5=0 | | 3(x+3)=2(x+9) | | 4-3(x-4)=x+8 | | x^3=2x+x^2 | | 5(y+2)=5y-2 | | 10b+-19=11 | | 4x-17=4(x-5) | | (h-7)(h+5)=-20 |

Equations solver categories