(x+5)(x+2)=(x+6)+(x-1)

Simple and best practice solution for (x+5)(x+2)=(x+6)+(x-1) 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+5)(x+2)=(x+6)+(x-1) equation:


Simplifying
(x + 5)(x + 2) = (x + 6) + (x + -1)

Reorder the terms:
(5 + x)(x + 2) = (x + 6) + (x + -1)

Reorder the terms:
(5 + x)(2 + x) = (x + 6) + (x + -1)

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = (x + 6) + (x + -1)
((2 * 5 + x * 5) + x(2 + x)) = (x + 6) + (x + -1)
((10 + 5x) + x(2 + x)) = (x + 6) + (x + -1)
(10 + 5x + (2 * x + x * x)) = (x + 6) + (x + -1)
(10 + 5x + (2x + x2)) = (x + 6) + (x + -1)

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = (x + 6) + (x + -1)

Reorder the terms:
10 + 7x + x2 = (6 + x) + (x + -1)

Remove parenthesis around (6 + x)
10 + 7x + x2 = 6 + x + (x + -1)

Reorder the terms:
10 + 7x + x2 = 6 + x + (-1 + x)

Remove parenthesis around (-1 + x)
10 + 7x + x2 = 6 + x + -1 + x

Reorder the terms:
10 + 7x + x2 = 6 + -1 + x + x

Combine like terms: 6 + -1 = 5
10 + 7x + x2 = 5 + x + x

Combine like terms: x + x = 2x
10 + 7x + x2 = 5 + 2x

Solving
10 + 7x + x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
10 + -5 + 7x + -2x + x2 = 5 + 2x + -5 + -2x

Combine like terms: 10 + -5 = 5
5 + 7x + -2x + x2 = 5 + 2x + -5 + -2x

Combine like terms: 7x + -2x = 5x
5 + 5x + x2 = 5 + 2x + -5 + -2x

Reorder the terms:
5 + 5x + x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
5 + 5x + x2 = 0 + 2x + -2x
5 + 5x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
5 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5x + x2 = 0 + -5
5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
5x + x2 = -5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5x + x2 = 1.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 2.5 = 1.118033989 Simplifying x + 2.5 = 1.118033989 Reorder the terms: 2.5 + x = 1.118033989 Solving 2.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.118033989 + -2.5 x = 1.118033989 + -2.5 Combine like terms: 1.118033989 + -2.5 = -1.381966011 x = -1.381966011 Simplifying x = -1.381966011

Subproblem 2

x + 2.5 = -1.118033989 Simplifying x + 2.5 = -1.118033989 Reorder the terms: 2.5 + x = -1.118033989 Solving 2.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.118033989 + -2.5 x = -1.118033989 + -2.5 Combine like terms: -1.118033989 + -2.5 = -3.618033989 x = -3.618033989 Simplifying x = -3.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.381966011, -3.618033989}

See similar equations:

| 2x+10=-70-8x | | 131-5x=4x+14 | | -35-2x=10-7x | | 65-3x=9x+17 | | 4x+14=84-3x | | a+a+7+3a+a-1=42 | | 18=3(x-6) | | 5+4x=20+x | | -10=2(3v+7) | | 2x+38=10x-58 | | -3=3(x+5) | | 12x-5=10x+5 | | 9x+8=4x+28 | | 6(p+4)-5(3+p)=12 | | -2(1+4x)=-26 | | 5x-22=23 | | 2x+24=8X | | -7(-3-8n)=21 | | 8(-n+2)=0 | | (y+1)(4y-25)=(2y-5)(2y-8) | | 6(1-3m)=-66 | | 24=8(a+6) | | -2(6+6x)=24 | | 6n+4=16 | | 2(6r+4)=-64 | | 83=a-912 | | 77=-7(x-5) | | wt=f | | x+313=235+99 | | 0=2(7k-7) | | 49=7(1+6n) | | 16f-14=9f-7 |

Equations solver categories