# Which quadratic equation is equivalent to (x + 2)^{2} + 5 (x + 2) – 6 = 0?

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

## Answer: The equivalent quadratic equation to (x + 2)^{2} + 5(x + 2) – 6 = 0 is x^{2} + 9x + 8 = 0.

Let us find an equivalent quadratic equation.

**Explanation:**

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} = a^{2} + 2ab + b^{2}

⇒ [x^{2} + 2 (x)(2) + 4] + [5x + 10] - 6 = 0

⇒ x^{2} + 4x + 4 + 5x + 10 - 6 = 0

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

⇒ x^{2} + (4 + 5) x + (10 - 6 + 4) = 0

⇒ x^{2} + 9x + 8 = 0

### Thus, x^{2} + 9x + 8 = 0 is the equivalent quadratic equation to (x + 2)^{2} + 5 (x + 2) – 6 = 0

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