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Solve the following quadratic equations

(i) 7x^{2} = 8 – 10x

(ii) 3(x^{2} – 4) = 5x

(iii) x(x + 1) + (x + 2) (x + 3) = 42

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#### Solution

(i) 7x^{2} = 8 – 10x

⇒ 7x^{2} + 10x – 8 = 0

⇒ 7x^{2} + 14x – 4x – 8 = 0

⇒ 7x(x + 2) – 4(x + 2) = 0

⇒ (x + 2) (7x – 4) = 0

⇒ x + 2 = 0 or 7x – 4 = 0

⇒ x = – 2 or x = 4/7

(ii) 3(x^{2} – 4) = 5x

⇒ 3x^{2} – 5x – 12 = 0

⇒ 3x^{2} – 9x + 4x –¬ 12 = 0

⇒ 3x(x – 3) + 4(x – 3) = 0

⇒ (x – 3) (3x + 4) = 0

⇒ x – 3 = 0 or 3x + 4 = 0

⇒ x = 3 or x = –4/3

(iii) x(x + 1) + (x + 2) (x + 3) = 42

⇒ x^{2} + x + x^{2} + 3x + 2x + 6 – 42 = 0

⇒ 2x^{2} + 6x – 36 = 0

⇒ x^{2} + 3x – 18 = 0

⇒ x^{2} + 6x – 3x – 18 = 0

⇒ x(x + 6) – 3(x + 6) = 0

⇒ (x + 6) (x – 3) = 0

⇒ x = – 6 or x = 3

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