x+x(x+1)+(x+2)=24

Simple and best practice solution for x+x(x+1)+(x+2)=24 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+x(x+1)+(x+2)=24 equation:


Simplifying
x + x(x + 1) + (x + 2) = 24

Reorder the terms:
x + x(1 + x) + (x + 2) = 24
x + (1 * x + x * x) + (x + 2) = 24
x + (1x + x2) + (x + 2) = 24

Reorder the terms:
x + 1x + x2 + (2 + x) = 24

Remove parenthesis around (2 + x)
x + 1x + x2 + 2 + x = 24

Reorder the terms:
2 + x + 1x + x + x2 = 24

Combine like terms: x + 1x = 2x
2 + 2x + x + x2 = 24

Combine like terms: 2x + x = 3x
2 + 3x + x2 = 24

Solving
2 + 3x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
2 + -24 + 3x + x2 = 24 + -24

Combine like terms: 2 + -24 = -22
-22 + 3x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-22 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 3x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 3x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 3x + x2 = 0 + 22
3x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
3x + x2 = 22

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 = 22 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + 3x + x2 = 24.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

x + 1.5 = 4.924428901 Simplifying x + 1.5 = 4.924428901 Reorder the terms: 1.5 + x = 4.924428901 Solving 1.5 + x = 4.924428901 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 = 4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.924428901 + -1.5 x = 4.924428901 + -1.5 Combine like terms: 4.924428901 + -1.5 = 3.424428901 x = 3.424428901 Simplifying x = 3.424428901

Subproblem 2

x + 1.5 = -4.924428901 Simplifying x + 1.5 = -4.924428901 Reorder the terms: 1.5 + x = -4.924428901 Solving 1.5 + x = -4.924428901 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 = -4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.924428901 + -1.5 x = -4.924428901 + -1.5 Combine like terms: -4.924428901 + -1.5 = -6.424428901 x = -6.424428901 Simplifying x = -6.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.424428901, -6.424428901}

See similar equations:

| 8x+8y=-16 | | 12.9+-2.2= | | 6x-6=4x+34 | | 12ax-y+2ay-6x= | | -8(2a+5)-4= | | 13.7+-0.1+-2.4= | | -3(-5p+8)-p= | | 2+7y=11-y-y | | 5x(5x+2)-(5x+2)= | | 6x-1=3x-43 | | 2(1-2y)+5y=3 | | 9y-2y+8=4y+38 | | 200-7x=95 | | 3025=x^2+.5625x^2 | | 5k-8=13-2k | | 2?5=-z?45 | | 10w-4w-w+2+w+9= | | 9x-(7x+6)=6 | | 2(3x-4)-10=5(x+4) | | (17x)^(1/2) | | 3025=x^2+1.7778x^2 | | 6=-1?2n | | f(x)=3sinx+4x-1 | | 6+(-3k)-24+13k-(-1)= | | 18y+1=67 | | 3x+8=2x+4fory | | 4x-15=-75 | | 3-3(7-8x)=0 | | 3-2(x+5)=17 | | (6s-5t)(6s+5t)= | | -9(4a+2)+4= | | y^2+1.7778y^2=3025 |

Equations solver categories