Mathematics 10 — Exercise 2.1 · Q1 (iv)

Full question

Write the following quadratic equation in standard form: 4 × (3 × x-2) = 9 × x².

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$12\times x-8-9\times x^2$$

2. Remove the brackets. A preceding minus sign reverses every sign inside that bracket.

   $$-9\times x^2+12\times x-8$$

3. Write EVERY distributed product before collecting terms.

   $$-8+12\times x-9\times x^2$$

4. Calculate this individual product, including its sign and powers.

   $$-8=-8$$

5. Calculate this individual product, including its sign and powers.

   $$12\times x=12\times x$$

6. Calculate this individual product, including its sign and powers.

   $$-9\times x^2=-9\times x^2$$

7. These terms have the same variable part. Add ONLY their coefficients.

   $$-8=-8$$

8. These terms have the same variable part. Add ONLY their coefficients.

   $$12=12$$

9. These terms have the same variable part. Add ONLY their coefficients.

   $$-9=-9$$

10. Put the simplified groups together.

    $$-8+12\times x-9\times x^2$$

11. Collect terms with the same power and simplify their coefficients.

    $$-9\times x^2+12\times x-8$$

12. Expand the brackets and subtract the right-hand terms from both sides. Collect powers of the variable.

    $$9\times x^2-12\times x+8=0$$

Answer

The final answer is shown below.