3x^2-11x-7=0

Simple and best practice solution for 3x^2-11x-7=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^2-11x-7=0 equation: 


Simplifying
3x2 + -11x + -7 = 0

Reorder the terms:
-7 + -11x + 3x2 = 0

Solving
-7 + -11x + 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'.
-2.333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -3.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -3.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + 2.333333333
-3.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-3.666666667x + x2 = 2.333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 2.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 2.333333333 + 3.361111114

Combine like terms: 2.333333333 + 3.361111114 = 5.694444447
3.361111114 + -3.666666667x + x2 = 5.694444447

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 5.694444447

Calculate the square root of the right side: 2.386303511

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 2.386303511 and -2.386303511.


Subproblem 1
x + -1.833333334 = 2.386303511

Simplifying
x + -1.833333334 = 2.386303511

Reorder the terms:
-1.833333334 + x = 2.386303511

Solving
-1.833333334 + x = 2.386303511

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 2.386303511 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 2.386303511 + 1.833333334
x = 2.386303511 + 1.833333334

Combine like terms: 2.386303511 + 1.833333334 = 4.219636845
x = 4.219636845

Simplifying
x = 4.219636845


Subproblem 2
x + -1.833333334 = -2.386303511

Simplifying
x + -1.833333334 = -2.386303511

Reorder the terms:
-1.833333334 + x = -2.386303511

Solving
-1.833333334 + x = -2.386303511

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -2.386303511 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -2.386303511 + 1.833333334
x = -2.386303511 + 1.833333334

Combine like terms: -2.386303511 + 1.833333334 = -0.552970177
x = -0.552970177

Simplifying
x = -0.552970177


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.219636845, -0.552970177}

See similar equations:

| x+2+2(x+2)=3x(x-2) | | 3x+8-x=16+4 | | 22c-17=12c+8 | | 8m=24+2m | | 7x^2+9+2=0 | | 5(x+3)-2x(x+3)=2x | | -x+7=6x+8 | | -30+27p=11p+2 | | 5x+35=13x-53 | | 14y-6=9y+24 | | x^2+5-6=0 | | -x-105=55+9x | | -x^3-x^2+21x+45=0 | | p-7=3p+11 | | 14-10x=106-38x | | 77-2x=2x+21 | | 4(2t+5)-22=7t-6 | | 5x-24=31 | | 10+4x+6=0 | | 3x+120=180 | | -8x-30=16-6x | | x-5=-8 | | 4f-27=-52 | | 6x+4=3x+1 | | 3a+8=a+19 | | log(x+5)+long(x)=20 | | 3x^3-2x-64=0 | | x-3=15+2x | | 4+x=8 | | 4x-151=-10x+45 | | x^2=-48y | | 5x(3x)=120 |

Equations solver categories