solve equation by method of your choice?

Well, you're almost fine so far, you have just slipped a sign going to the last line

2x^2 + 5x = 0

Now we can factorise
x(2x-5) = 0

So either x=0 or 2x + 5 = 0

So we have 2x = -5, so x = -5/2

So there you are x = -5/2, 0 :-)

x^2+x= 4 - x^2 -4x -4
x^2+x= -x^2 - 4x
2x^2 = -5x (correct up to here)
2x^2 + 5x = 0
x(2x + 5) = 0
x = 0, -5/2

You`ve got the answer !
x² + x = 4 - (x² + 4x + 4)
x² + x - 4 = - x² - 4x - 4
2x² + 5x = 0
x (2x - 5) = 0
x = 0 , x = - 5/2

x(x + 1) = 4 - (x + 2)(x + 2)
x*x + x*1 = 4 - (x*x + 2*x + x*2 + 2*2)
x^2 + x = 4 - (x^2 + 2x + 2x + 4)
x^2 + x = 4 - x^2 - 2x - 2x - 4
x^2 + x^2 + x + 2x + 2x - 4 + 4 = 0
2x^2 + 5x = 0
x(2x + 5) = 0

x = 0

2x + 5 = 0
2x = -5
x = -5/2 (-2.5)

∴ x = -5/2 (-2.5) , 0

First, let's work on the left hand side of your equation, the x(x+1)
This means, for instance, to see if it can be simplified at all.
x+1 evaluates to x+1
Multiply x by x+1
we multiply x by each term in x+1 term by term.
This is the distributive property of multiplication.
Multiply x and x
Multiply the x and x
Multiply x and x
Combine the x and x by adding the exponents, and keeping the x, to get
The answer is
x × x =
Multiply x and 1
Multiply x and 1
The x just gets copied along.
The answer is x
x
x × 1 = x
x*(x+1) evaluates to
So, all-in-all, the left hand side of your equation can be written as:
Now, let's work on the right hand side of your equation, the 4
- (x+2)(x+2)
x+2 evaluates to x+2
x+2 evaluates to x+2
Multiplying x+2 by x+2 is a classic Algebra problem. Here, you are trying
to multiply two binomials together (two expressions that each contain two terms).
Your book might call this finding the "Product of Two Binomials".
To work this problem, we'll use the "F.O.I.L." method. F.O.I.L. stands
for First, Outer, Inner, Last.
First, we'll multiply the two First terms, the x and x together.
Multiply x and x
Multiply the x and x
Multiply x and x
Combine the x and x by adding the exponents, and keeping the x, to get
The answer is
x × x =
Second, we'll multiply the two Outer terms, the x and 2 together.
Multiply x and 2
Multiply x and 1
The x just gets copied along.
The answer is x
x
x × 2 = 2x
Third, we'll multiply the two Inner terms, the 2 and x together.
Multiply 2 and x
Multiply 1 and x
The x just gets copied along.
x
2 × x = 2x
2x combines with 2x to give 4x
Lastly, we'll multiply the two Last terms, the 2 and 2 together.
Multiply 2 and 2
1
2 × 2 = 4
(x+2)*(x+2) evaluates to
4 - 4 = 0
The answer is
4-(x+2)*(x+2) evaluates to
The right hand side of your equation can be written as:
So with these (any) simplifications, the equation we'll set out
to solve is:
=
Move the to the left hand side by adding to both sides, like this:
To the left hand side:
+ =
The answer is
To the right hand side:
+ =
The answer is -4x
Now, the equation reads:
= -4x
Move the -4x to the left hand side by adding 4x to both sides, like this:
To the left hand side:
x + 4x = 5x
The answer is
To the right hand side:
-4x + 4x = 0x
The answer is 0
Now, the equation reads:
= 0

x(x+1) = 4 - (x + 2) (x + 2)
x^2 + x = 4 - (x^2 + 4x + 4)
x^2 + x = 4 - x^2 - 4x - 4
x^2 + x = -x^2 - 4x
(x^2 + x )(1/x) = (-x^2 - 4x)(1/x)
x + 1 = -x - 4
2x = -5
x = -5/2

woops you meant
2x^2 + 5x = 0

now keep going!
x(2x+5) = 0
x -5/2 , 0