x=4x+x^2-12

Simple and best practice solution for x=4x+x^2-12 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=4x+x^2-12 equation:


Simplifying
x = 4x + x2 + -12

Reorder the terms:
x = -12 + 4x + x2

Solving
x = -12 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
12 + x + -4x + -1x2 = -12 + 4x + x2 + 12 + -4x + -1x2

Combine like terms: x + -4x = -3x
12 + -3x + -1x2 = -12 + 4x + x2 + 12 + -4x + -1x2

Reorder the terms:
12 + -3x + -1x2 = -12 + 12 + 4x + -4x + x2 + -1x2

Combine like terms: -12 + 12 = 0
12 + -3x + -1x2 = 0 + 4x + -4x + x2 + -1x2
12 + -3x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
12 + -3x + -1x2 = 0 + x2 + -1x2
12 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + 3x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 3x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 3x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3x + x2 = 0 + 12
3x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
3x + x2 = 12

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 = 12 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + 3x + x2 = 14.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + 1.5 = 3.774917218 Simplifying x + 1.5 = 3.774917218 Reorder the terms: 1.5 + x = 3.774917218 Solving 1.5 + x = 3.774917218 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 = 3.774917218 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.774917218 + -1.5 x = 3.774917218 + -1.5 Combine like terms: 3.774917218 + -1.5 = 2.274917218 x = 2.274917218 Simplifying x = 2.274917218

Subproblem 2

x + 1.5 = -3.774917218 Simplifying x + 1.5 = -3.774917218 Reorder the terms: 1.5 + x = -3.774917218 Solving 1.5 + x = -3.774917218 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 = -3.774917218 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.774917218 + -1.5 x = -3.774917218 + -1.5 Combine like terms: -3.774917218 + -1.5 = -5.274917218 x = -5.274917218 Simplifying x = -5.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.274917218, -5.274917218}

See similar equations:

| n^2+4n+8=8 | | 3.7y-1.9y-31.5=13.5 | | 48=3x+6(x-4) | | 6-4y=y^2-6 | | 9m^2-17m-2=0 | | 6(H+7)-4=10 | | -9x+19=100 | | -v+7+4v=6+5v+4 | | x+x+7+x-3=52 | | 2/5(10x-5)=-38 | | -5(1-5x)+5(-8x-2)=-4x-84 | | 0.75x+20=65 | | -5x-(6+-4x)=21 | | 4x+(3x-5)=100 | | -3(b-3)+6=-b+13 | | 6x(-1/2)-3 | | 20=0.555f-17.777777776 | | 35=5/7v | | 7overx=12 | | -2b+-7=-7 | | 9=3/5x-3 | | y=1000+0.03x | | 40+40+110+4x+x=540 | | 3(2Y^2/2)=5X-5 | | a-19=-26 | | 7/17=x/10 | | 5(s+4)=45 | | -4b-2=-6b-18 | | 84h-48h=216 | | 11x-5y=5y-6 | | 9*3/5 | | a-4/5=84/7 |

Equations solver categories