3x^2=7x+11

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


Simplifying
3x2 = 7x + 11

Reorder the terms:
3x2 = 11 + 7x

Solving
3x2 = 11 + 7x

Solving for variable 'x'.

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

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

Combine like terms: 11 + -11 = 0
-11 + -7x + 3x2 = 0 + 7x + -7x
-11 + -7x + 3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-11 + -7x + 3x2 = 0

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

Divide each side by '3'.
-3.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 3.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 3.666666667 + 1.361111112

Combine like terms: 3.666666667 + 1.361111112 = 5.027777779
1.361111112 + -2.333333333x + x2 = 5.027777779

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 5.027777779

Calculate the square root of the right side: 2.242270675

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.242270675 and -2.242270675.


Subproblem 1
x + -1.166666667 = 2.242270675

Simplifying
x + -1.166666667 = 2.242270675

Reorder the terms:
-1.166666667 + x = 2.242270675

Solving
-1.166666667 + x = 2.242270675

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 2.242270675 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 2.242270675 + 1.166666667
x = 2.242270675 + 1.166666667

Combine like terms: 2.242270675 + 1.166666667 = 3.408937342
x = 3.408937342

Simplifying
x = 3.408937342


Subproblem 2
x + -1.166666667 = -2.242270675

Simplifying
x + -1.166666667 = -2.242270675

Reorder the terms:
-1.166666667 + x = -2.242270675

Solving
-1.166666667 + x = -2.242270675

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -2.242270675 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -2.242270675 + 1.166666667
x = -2.242270675 + 1.166666667

Combine like terms: -2.242270675 + 1.166666667 = -1.075604008
x = -1.075604008

Simplifying
x = -1.075604008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.408937342, -1.075604008}

See similar equations:

| 3(2x-1)-11=-2(2-x) | | 3f^2-14f+8=0 | | X+10x+14=0 | | 3x-4-2x=-5x+2 | | k^2-11k=0 | | 4x-6(x-1)=-8 | | 3x+4+2x+5= | | 5x+10=2x+2 | | 3j^2-4j-7=0 | | 14-(x+x)=3(x+9)-10 | | 121r^2-64t^2=0 | | 14-1x+15=3x+9 | | g^2+41g=0 | | u^2+49u=0 | | 75=6x+4x+6 | | 2b=8b-80 | | k^2-37k=0 | | 8j-41=31 | | p^2-6p=0 | | 2u-17=3 | | 10a-46=44 | | s^2+9s-22=0 | | (2n^2-3n+6)(7n-8)= | | 7(2h+3)=-22-9h | | k^2+36k=0 | | 2.8x=64 | | s^2-44s=0 | | 2(8v-1)=13+v | | (4n^2-7n-4)(2n+8)= | | =(8k-3)(8k+3) | | (5x^2-3x+2)(6x-2)= | | =3d+4e-2e+6d |

Equations solver categories