solve for x. help please? anyone good?

Question

1. x^2 - 4x - 5 = 0

2. x^2 +6x + 5 = 0

3. x^2 -6x + 5 = 0

4. x^2 +4x - 5 = 0

Answer 1

1.
x^2 - 4x - 5 = 0
x^2 - 5x + x - 5 = 0
(x^2 - 5x) + (x - 5) = 0
x(x - 5) + (x - 5) = 0
(x - 5)(x + 1) = 0
now set each one =0 and solve
x - 5 = 0
x = 5

x + 1 = 0
x = -1

2. x^2 +6x + 5 = 0
x^2 + x + 5x + 5 = 0
(x^2 + x) + (5x + 5) = 0
x(x + 1) + 5(x + 1) = 0
(x + 1)(x + 5) = 0
now set each =0 and solve for x.

3. x^2 -6x + 5 = 0
x^2 - x - 5x + 5 = 0
(x^2 - x) - (5x - 5) = 0
x(x - 1) - 5(x - 1) = 0
(x - 1)(x - 5) = 0
now solve

4. x^2 +4x - 5 = 0
x^2 + 5x - x - 5 = 0
(x^2 + 5x) - (x + 5) = 0
x(x + 5) - (x + 5) = 0
(x + 5)(x - 1) = 0
now solve

Answer 2

1. x^2 - 4x - 5 = 0 - factorise
(x - 5)(x + 1) =0
x- 5 = 0 therefore x = 5 &
x + 1 = 0 therefore x = -1

2. x^2 + 6x + 5 = 0 - factorise
(x + 5 )(x + 1 ) = 0
x + 5 = 0 therefore x = -5 &
x + 1 = 0 therefore x = -1

3. x^2 - 6x + 5 = 0 - factorise
(x - 5)(x -1) = 0
x - 5 = 0 therefore x = 5
x - 1 = 0 therefore x = 1

4. x^2 +4x - 5 = 0 - factorise
(x + 5)(x -1) = 0
x + 5 = 0 therefore x = -5
x - 1 = 0 therefore x = 1

Answer 3

1)
x^2 - 4x - 5 = 0
(x-5)(x+1) = 0 -> a
x = 5 , -1

2)
x^2 +6x + 5 = 0
(x+5)(x+1) = 0 -> b
x = -5, -1

3)
x^2 -6x + 5 = 0
(x-5)(x-1) = 0 -> c
x = 5, 1

4)
x^2 +4x - 5 = 0
(x+5)(x-1) = 0 -> d
x = -5, 1

In order to get the expression in a, b, c, d in the above, you can do few simple steps to achieve it.
Using example in Q1) x^2 - 4x - 5 = 0
(i) Place x^2 on the left hand side (LHS),
(ii) Place -4x in the centre,
(iii) Place -5 on the right hand side(RHS).
(iv)Looking at the LHS, in order to get x^2, you multiply x and x. Thus, place one of the x on top of another x.
(v)Looking at the centre and RHS, in order to achieve -5, you will need to multiply -5 and 1. Thus, place -5 on top of 1.
(vi)Now, when you cross multiply, you will get x * -5 and x * 1, and therefore -5x on top of x. When you add them up, you will get -4x which is what you need on the RHS.
(vii)Thus, looking from left to right on the same row, the equation will be (x-5) and (x+1) respectively.

The same method is used for Q2, Q3, Q4