3x^2-41x+105=0

Simple and best practice solution for 3x^2-41x+105=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^2-41x+105=0 equation:


Simplifying
3x2 + -41x + 105 = 0

Reorder the terms:
105 + -41x + 3x2 = 0

Solving
105 + -41x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
35 + -13.66666667x + x2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -13.66666667x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -13.66666667x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -13.66666667x + x2 = 0 + -35
-13.66666667x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-13.66666667x + x2 = -35

The x term is -13.66666667x.  Take half its coefficient (-6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
-13.66666667x + 46.69444447 + x2 = -35 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667x + x2 = -35 + 46.69444447

Combine like terms: -35 + 46.69444447 = 11.69444447
46.69444447 + -13.66666667x + x2 = 11.69444447

Factor a perfect square on the left side:
(x + -6.833333335)(x + -6.833333335) = 11.69444447

Calculate the square root of the right side: 3.419714092

Break this problem into two subproblems by setting 
(x + -6.833333335) equal to 3.419714092 and -3.419714092.

Subproblem 1

x + -6.833333335 = 3.419714092 Simplifying x + -6.833333335 = 3.419714092 Reorder the terms: -6.833333335 + x = 3.419714092 Solving -6.833333335 + x = 3.419714092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = 3.419714092 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 3.419714092 + 6.833333335 x = 3.419714092 + 6.833333335 Combine like terms: 3.419714092 + 6.833333335 = 10.253047427 x = 10.253047427 Simplifying x = 10.253047427

Subproblem 2

x + -6.833333335 = -3.419714092 Simplifying x + -6.833333335 = -3.419714092 Reorder the terms: -6.833333335 + x = -3.419714092 Solving -6.833333335 + x = -3.419714092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = -3.419714092 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -3.419714092 + 6.833333335 x = -3.419714092 + 6.833333335 Combine like terms: -3.419714092 + 6.833333335 = 3.413619243 x = 3.413619243 Simplifying x = 3.413619243

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.253047427, 3.413619243}

See similar equations:

| 4(3x+2)+3=3(2x-5)+5 | | z^2+4iz+6=0 | | 8(2x+4)=3(-3x-6) | | 21+21+32=180 | | 26-2x=2x-10 | | 9x-12=x+20 | | x=4+5x | | 6x^2+17x+29=0 | | X-9=45-6x | | X-3=x+27 | | 10(4x-4)-8(4x+5)=-56 | | x+3=4x+8 | | X=2+4x-3 | | 3xy+2x-2y=0 | | 5x+8-9x+3+4x= | | X-5=70-6x | | 6x^2-58x+99=0 | | 15x+9x-1=7x+3 | | 4m+6=6-2m | | ax+2a^2=0 | | 5r^2+3r=14.81 | | 6sin^2x+sin=4 | | -0.391+23.94x=-3.2(0.43x-2.3) | | 4v+6=5v-8 | | 2X^2+13x+5=0 | | x-7(1.34+0.32x)=0.01x | | 3(-2)=9 | | 9(x+4)=3(x+26) | | Y=-0.2x^2+5 | | X^5-6x^3-8x-1=0 | | 46=g+-8 | | 5x-4=86-10x |

Equations solver categories