1. First, expand the brackets on the left-hand side of the equation.
2. Rearrange the equation so that all terms are on one side, equal to zero. This will give you a standard quadratic equation in the form ax² + bx + c = 0.
3. Solve the resulting quadratic equation. You can do this by either factorising, completing the square, or using the quadratic formula.
4. Remember that a quadratic equation usually has two solutions.
Full Answer
The given equation is (x + 2)(x - 5) = 6x.
**1. Expand the brackets:**
We use the FOIL method (First, Outer, Inner, Last):
(x * x) + (x * -5) + (2 * x) + (2 * -5)
= x² - 5x + 2x - 10
Combine the x terms:
= x² - 3x - 10
So the equation is now: x² - 3x - 10 = 6x
**2. Rearrange to standard quadratic form (ax² + bx + c = 0):**
Subtract 6x from both sides:
x² - 3x - 6x - 10 = 0
x² - 9x - 10 = 0
**3. Solve the quadratic equation:**
We can factorise this expression. We are looking for two numbers that multiply to give -10 and add to give -9. These numbers are -10 and +1.
So, the equation becomes:
(x - 10)(x + 1) = 0
This gives two possible solutions:
- If x - 10 = 0, then x = 10.
- If x + 1 = 0, then x = -1.
The solutions are x = 10 and x = -1.
Common mistakes
✗ Errors in expanding the brackets, especially with negative signs.
✗ Incorrectly rearranging the equation (e.g., adding 6x instead of subtracting).
✗ Errors in factorising or in applying the quadratic formula.
✗ Finding only one of the two solutions.
Expert