Which quadratic equation is equivalent to (x + 2)² + 5 (x + 2) - 6 = 0?

Solution:

An equation is in the form  ax² + bx + c = 0 is called a quadratic equation, where a ≠ 0 . It has a degree equal to 2.

To find the equivalent equation, we need to simplify the given quadratic equation.

⇒ (x + 2)² + 5(x + 2) - 6 = 0

By using algebraic identity (a + b)² = a² + 2ab + b²

⇒  [x² + 2 (x)(2) + 4] + [5x + 10] - 6 = 0 

⇒ x² + 4x + 4 + 5x + 10 - 6 = 0

By adding the coefficents of x and constant terms separately, we get

⇒ x² + (4 + 5) x + (10 - 6 + 4) = 0

⇒ x² + 9x + 8 = 0

Thus, x² + 9x + 8 = 0 is the equivalent quadratic equation to (x + 2)² + 5 (x + 2) - 6 = 0

Which quadratic equation is equivalent to (x + 2)² + 5 (x + 2) - 6 = 0?

Summary:

The equivalent quadratic equation to (x + 2)² + 5(x + 2) - 6 = 0 is x² + 9x + 8 = 0.