Mathematics 10 — Exercise 2.1 · Q1 (i)

Full question

Write the following quadratic equation in standard form: 3 × x-1 = 2 × x².

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$3\times x-1-2\times x^2$$

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

   $$-2\times x^2+3\times x-1$$

3. Write EVERY distributed product before collecting terms.

   $$-1+3\times x-2\times x^2$$

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

   $$-1=-1$$

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

   $$3\times x=3\times x$$

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

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

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

   $$-1=-1$$

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

   $$3=3$$

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

   $$-2=-2$$

10. Put the simplified groups together.

    $$-1+3\times x-2\times x^2$$

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

    $$-2\times x^2+3\times x-1$$

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

    $$2\times x^2-3\times x+1=0$$

Answer

The final answer is shown below.