Answered

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Richie is solving the equation x^2 −12x = 28 by completing the square. What number should he add to both sides of the equation to complete the square? A) 6 B) 12 C) 36 D) 64

Sagot :

Given,

The equation is, x^2-12x=28.

Comapring the given equation with

[tex](a-b)^2=a^2-2ab+b^2[/tex]

On comapring it obtains that,

[tex]\begin{gathered} a^2=x^2 \\ a=x\ldots\text{.}(1) \end{gathered}[/tex]

Similarly,

[tex]\begin{gathered} -2ab=-12x \\ -2\times x\times b=-12x \\ b=\frac{-12x}{-2x} \\ b=6 \end{gathered}[/tex]

Now,

[tex]b^2=6\times6=36[/tex]

Hence, 36 is added to both sides to make the equation complete square.

Hence, option d is correct

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