Question

How do you solve `4x^2 + 4x - 3 = 0` by factoring?

Answer 1

The solutions for the equation are
`color(blue)(x=-3/2, x=1/2`

Explanation:

`4x^2+4x−3`

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 4*(-3) = -12`
and
`N_1 +N_2 = b = 4`

After trying out a few numbers we get `N_1 = 6` and `N_2 =-2`
`6*(-2) = -12`, and `6+(-2)= 4`

`4x^2+color(blue)(4x)−3 =4x^2-color(blue)(2x +6x)−3`

`=2x(2x-1) +3(2x-1)`

`color(blue)((2x+3)(2x-1)` is the factorised form of the expression.

Now we can equate each of the two factors to zero and find the solutions.

`2x+3 = 0, color(blue)(x=-3/2`
`2x-1=0, color(blue)(x=1/2`