Question

Complete the square to transform the expression x2 6x 5 into the form a(x − h)2 k. (x 6)2 4 (x 6)2 − 4 (x 3)2 − 4 (x 3)2 4

Answer 1

An equation is formed of two equal expressions. The equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The transformation of the equation from x²+6x+5 into the form a(x − h)²+k can be done in the following steps as shown below,

1. Taking +5 on the right-hand side of the equation,

$x^2+6x+5 = 0\\\\x^2+6x = -5$

2. Now if we add +9 on both sides of the equation, we will get,

$x^2+6x = -5\\\\x^2+6x+9 = -5+9$

3. Now we look at the left side of the equation as the square of the binomial expression (x+3).

$x^2+6x+9 = -5+9\\\\(x+3)^2 =4$

4. Taking +4 from the right side of the equation to the left side of the equation,

$(x+3)^2 =4\\\\(x+3)^2 -4=0$

Thus, the equation is in the form of a(x − h)²+k, where the value of a is 1, h is -3 and the value of k is -4.

Hence, the equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.

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