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:
x2 = 2 + -3x

Solving
x2 = 2 + -3x

Solving for variable 'x'.

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

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

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

Combine like terms: -3x + 3x = 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:

| 4x^2+15x-2=0 | | (2.4-2v)/3=9 | | (3x-5.7)-6=4.1 | | 3(x-2)=5(x-4) | | (3x-5.7)/6=4.1 | | (y+x)(y-x)=2x | | (8-n)-7=4/3 | | 9w+17=6w+32 | | (8-n)/7=4/3 | | Y+x= | | y+x*y-x=2x | | -3(2s-2)-6=-3(9s+1)-4 | | (7+3s)/4=5/2 | | f(x)=49 | | (7+3s)/4+5/2 | | 36=9a | | 5w-13=7 | | Y=-6-2y | | (7t-2)-(-3G+1)=-3(1-3t) | | 5r+32=8r+17 | | 6-3x=x-12 | | 6+5=45 | | x^1/2(x^2/3+x^5/3) | | P-p-6=0 | | -2=w/-14 | | 3(2x-2)+2(1-x)=12 | | 3x+8y=48 | | 9a=630 | | x^2+12x-11=0 | | 2(x-2)=x+4 | | R=1-3d(60-t) | | x-12=y |

Equations solver categories