x^2+3x=2

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


Simplifying
x2 + 3x = 2

Reorder the terms:
3x + x2 = 2

Solving
3x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 3x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x + x2 = 0 + 2
3x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3x + x2 = 2

The x term is 3x.  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.
3x + 2.25 + x2 = 2 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3x + x2 = 4.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + 1.5 = 2.061552813

Simplifying
x + 1.5 = 2.061552813

Reorder the terms:
1.5 + x = 2.061552813

Solving
1.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.061552813 + -1.5
x = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
x = 0.561552813

Simplifying
x = 0.561552813


Subproblem 2
x + 1.5 = -2.061552813

Simplifying
x + 1.5 = -2.061552813

Reorder the terms:
1.5 + x = -2.061552813

Solving
1.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.061552813 + -1.5
x = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
x = -3.561552813

Simplifying
x = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.561552813, -3.561552813}

See similar equations:

| 4-3b=-23 | | 17a-(5a+10)=14 | | 29=11+3s | | x^2+6x=-15 | | 5n^2+18n-8=0 | | x-5+8=3 | | 7x+9=-3x+4 | | 2x-11=-23 | | 6+4c=18 | | 4[64]= | | 2x+2(11-4x)=82+x | | 2m+3(m-1)=17 | | 3(2x+7)=15(x-4) | | -2x+7+3x=11 | | x+12=2x-16 | | 4.5x+8=10x-2 | | 33+15w=3e-e+4e | | 3(15)-14=2(15)+1 | | 24=-5x+7x+2 | | 8-2(x+3)= | | 4y+12=30 | | 2x-63=153 | | y=-2(x+3)(x-5) | | 62=4b+2 | | 0.378+s=2.918 | | y=-2x^2+4x+30 | | 5x+17=82 | | 55.7+b=32.119 | | 3x+12=-48 | | 30x^3+7x-2=0 | | -5x-18= | | 17.52-z=4.13 |

Equations solver categories