3x^2-105x+3=0

Simple and best practice solution for 3x^2-105x+3=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^2-105x+3=0 equation: 


Simplifying
3x2 + -105x + 3 = 0

Reorder the terms:
3 + -105x + 3x2 = 0

Solving
3 + -105x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -35x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -35x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -35x + x2 = 0

Solving
1 + -35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -35x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -35x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -35x + x2 = 0 + -1
-35x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-35x + x2 = -1

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -1 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -1 + 306.25

Combine like terms: -1 + 306.25 = 305.25
306.25 + -35x + x2 = 305.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 305.25

Calculate the square root of the right side: 17.47140521

Break this problem into two subproblems by setting 
(x + -17.5) equal to 17.47140521 and -17.47140521.


Subproblem 1
x + -17.5 = 17.47140521

Simplifying
x + -17.5 = 17.47140521

Reorder the terms:
-17.5 + x = 17.47140521

Solving
-17.5 + x = 17.47140521

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 17.47140521 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 17.47140521 + 17.5
x = 17.47140521 + 17.5

Combine like terms: 17.47140521 + 17.5 = 34.97140521
x = 34.97140521

Simplifying
x = 34.97140521


Subproblem 2
x + -17.5 = -17.47140521

Simplifying
x + -17.5 = -17.47140521

Reorder the terms:
-17.5 + x = -17.47140521

Solving
-17.5 + x = -17.47140521

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -17.47140521 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -17.47140521 + 17.5
x = -17.47140521 + 17.5

Combine like terms: -17.47140521 + 17.5 = 0.02859479
x = 0.02859479

Simplifying
x = 0.02859479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.97140521, 0.02859479}
Solution
x = {34.97140521, 0.02859479}

See similar equations:

| 2(4x+4)=-5(4x-5) | | -3(x+2)-43=4-29 | | -2x^2-6x=-20 | | 6-6=16x+5x | | 17+12b-9=3b+37 | | 3(x-2)+1=2(x-1)+3x-5 | | 7y=y+24 | | F(x)=x^4-2x^3-7x+20x-12 | | y=-2.1x^2+53x+150 | | 4y+7=2y-5 | | -3(3p+5)-2(1-11p)=3(8+2p) | | 10-6(8x-2)=9x-(3+4) | | X^2*(x-7)=64 | | 48/75 | | 2x^3+2x^2+90=0 | | -36z=144 | | (13b-3)-4(3b+4)=-5 | | 25x+9y=49.27 | | x^2+6x=10x | | 3m^2-10m-48=0 | | x+5x-8=x+6-3 | | -3(7p+4)-2(2-17p)=3(8+4p) | | -3(7p+4)-2(2-17p)=3 | | 2x+12x-14=0 | | 12x/6y=24 | | -4k+y=4 | | 3b=700 | | 4x^(1/2) | | d+j= | | (x)=3x+8 | | (6x+60)=4x+20 | | (6x+60)= |

Equations solver categories