Solve the equations by factorisation: 6x² – 150 = 0

To solve the equation 6x² – 150 = 0 by factorisation, we first want to simplify the equation.

Start by moving the constant term to the other side:

6x² = 150

Next, divide both sides by 6:

x² = 25

Now, we can take the square root of both sides:

x = ±5

Thus, the solutions to the equation are x = 5 and x = -5.

For factorisation, we can also write the original equation 6x² – 150 as:

6(x² - 25) = 0

Notice that x² – 25 is a difference of squares, which can be factored as:

(x - 5)(x + 5)

Therefore, we can rewrite the equation as:

6(x - 5)(x + 5) = 0

Setting each factor to zero gives us the same solutions:

x - 5 = 0  or  x + 5 = 0

Thus, the final solutions are:

• x = 5
• x = -5