Mathematics 10 — Exercise 2.1 · Q1 (iii)

Full question

Write the following quadratic equation in standard form: 2 × x²-4 × x = 4 × x+7.

Step-by-step solution

1. Substitute the function expressions, keeping the brackets.

   $$2\times x^2-4\times x-4\times x+7$$

2. Distribute each bracket product: each term multiplies every term in the other bracket.

   $$2\times x^2-8\times x-7$$

3. Write EVERY distributed product before collecting terms.

   $$-4\times x+2\times x^2-7-4\times x$$

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

   $$-4\times x=-4\times x$$

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

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

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

   $$\left(-1\right)\times 7=-7$$

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

   $$-4\times x=-4\times x$$

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

   $$-4-4=-8$$

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

   $$2=2$$

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

    $$-7=-7$$

11. Put the simplified groups together.

    $$-8\times x+2\times x^2-7$$

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

    $$2\times x^2-8\times x-7$$

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

    $$2\times x^2-8\times x-7=0$$

Answer

The final answer is shown below.