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What value of c will make the
expression
x² + 6x + 4 + c a perfect
square?

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Value Square

What value of c will make the expression x² + 6x + 4 + c a perfect square?

Solution:

- Square = x² + 6x + 4 + c

- Square = c + x² + 6x + 4 =
- c + x² + 6x + 4 + (9) - (9)

Complete the square:

- Square = c - 5 + (x² + 6x + 9) =
- c - 5 + (x + 3)²

Hence, the correct answer is Square = c + x² + 6x + 4 = c. + (x + 3)² - 5 or c = 5

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$$c= 5$$

Step-by-step explanation:

$$\text{If any quadratic expression is a perfect square, then}\\ \\~~~~~~~\text{discriminant} = 0\\\\\implies b^2 -4ac = 0\\\\\implies 6^2 - 4 \cdot 1 (4+c) = 0~~~~~~~~~~~~~~~;[\text{Compare with the standard form}~ ax^2 +bx +c]\\\\\implies 36 - 16 - 4c =0 \\\\\implies 20-4c =0\\\\\implies 4c = 20\\\\\implies c = \dfrac{20}{4}\\\\\implies c= 5$$
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