Question

Solve the following quadratic equation.

(2x + 3)² = 25

Answer 1

(2x + 3)² = 25

⇒ 4x² + 12x + 9 = 25

⇒ 4x² + 12x + 9 − 25 = 0

⇒ 4x² + 12x − 16 = 0

Dividing whole equation by 4,

⇒ x² + 3x − 4 = 0

⇒ x² + 4x − x − 4 = 0

⇒ x(x + 4) − 1(x + 4) = 0

⇒ (x + 4)(x − 1) = 0

⇒ x = 1, −4.

Answer 2

(2x + 3)² = 25

∴ (2x + 3)² – 25 = 0

∴ (2x + 3)² – (5)² = 0

∴ (2x + 3 – 5)(2x + 3 + 5) = 0   ...[∵ a² – b = (a – b)(a + b)]

∴ (2x – 2)(2x + 8) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get,

∴ 2x – 2 = 0 or 2x + 8 = 0

∴ 2x = 2 or 2x = –8

∴ x = `2/2` or x = `(–8)/2`

∴ x = 1 or x = –4

∴ The roots of the given quadratic equation are 1 and –4.