12x+24=x^2-x

Simple and best practice solution for 12x+24=x^2-x 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 12x+24=x^2-x equation:


Simplifying
12x + 24 = x2 + -1x

Reorder the terms:
24 + 12x = x2 + -1x

Reorder the terms:
24 + 12x = -1x + x2

Solving
24 + 12x = -1x + x2

Solving for variable 'x'.

Combine like terms: 12x + x = 13x
24 + 13x + -1x2 = -1x + x2 + x + -1x2

Reorder the terms:
24 + 13x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
24 + 13x + -1x2 = 0 + x2 + -1x2
24 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 13x + -1x2 = 0

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

Divide each side by '-1'.
-24 + -13x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -13x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -13x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -13x + x2 = 0 + 24
-13x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-13x + x2 = 24

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 24 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 24 + 42.25

Combine like terms: 24 + 42.25 = 66.25
42.25 + -13x + x2 = 66.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(x + -6.5) equal to 8.139410298 and -8.139410298.

Subproblem 1

x + -6.5 = 8.139410298 Simplifying x + -6.5 = 8.139410298 Reorder the terms: -6.5 + x = 8.139410298 Solving -6.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.139410298 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.139410298 + 6.5 x = 8.139410298 + 6.5 Combine like terms: 8.139410298 + 6.5 = 14.639410298 x = 14.639410298 Simplifying x = 14.639410298

Subproblem 2

x + -6.5 = -8.139410298 Simplifying x + -6.5 = -8.139410298 Reorder the terms: -6.5 + x = -8.139410298 Solving -6.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.139410298 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.139410298 + 6.5 x = -8.139410298 + 6.5 Combine like terms: -8.139410298 + 6.5 = -1.639410298 x = -1.639410298 Simplifying x = -1.639410298

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.639410298, -1.639410298}

See similar equations:

| 0.3=6 | | 66+90+8x=180 | | (y-5)=-3(x+2) | | 5.3-6m=1.3 | | -15.00+(12.00x)=-123 | | 5x-18=2x+6 | | 5-7(-5m+3)=-156 | | 15-3n=n+1 | | 0=12x^2+12x-4 | | 7.2(11.8n-9.3)+2.1=9.6n+9.4(1+3.2n) | | 3z+4z=6z+9 | | x+3+49=180 | | 9-3v=24 | | 7(4x+5)=147 | | 0=x^2-13x+24 | | 6x+x-6=6x+3 | | u^4-2u^2-63=0 | | 0=4x^3+6x^2-4x | | 8x+18y=12 | | 4-(6x+6)=(-2x+10) | | m^4-7m-8=0 | | 8v=136 | | -22x+60=8x+60 | | 36v^3-42v^2-6v+7=0 | | -8+7x=5x-2 | | 363-8382x(h-77)=w | | 5x+7-3x=4x+9 | | 46+13+x=90 | | 4w+3v= | | 24.2=w+6.2 | | 6v^2-1=0 | | y=1.25x-10 |

Equations solver categories