# How to Solve the Quadratic Equation by Factoring

Solve the quadratic equation **√( x – 2) + √(4 – x) = √(6 – x)** by factoring

## Solution

√(*x* – 2) + √(4 – *x*) = √(6 – *x*)

Square both sides then

(*x* – 2) + 2 × √(*x* – 2) × √(4 – *x*) + (4 – *x*) = 6 – *x*

We can rearrange this equation

2 + 2 × √(*x* – 2) × √(4 – *x*) = 6 – *x*

⇒ 2 × √(*x* – 2) × √(4 – *x*) = 4 – *x*

Again square both sides

2 × (*x* – 2) × (4 – *x*) = (4 – *x*)²

⇒ (4 – *x*)² – 4 × (*x* – 2) × (4 – *x*) = 0

## We can solve this quadratic equation by factoring

⇒ (4 – x) (4 – x – 4(x – 2)) = 0

so, (4 – x) (4 – x – 4x + 8) = 0

Then, (4 – x)(-5x + 12) = 0

Now we got **(4 – x) **and** (-5x + 12)** is the factors of the quadratic equation

then

**4 – x = 0** or **-5x + 12 = 0**

so **x = 4, 12/5**