Solve the equation x(x – 2) = 24.
A. Solve the equation by factoring. (1 point)
B. Solve the equation by completing the square.

Question

Solve the equation x(x – 2) = 24.
A. Solve the equation by factoring. (1 point)
B. Solve the equation by completing the square.

zepp · Answer

Your equation could be written as $$\large x^2-2x=24\\large x^2-2x-24=0$$

Then you'd have to factorize it

zepp · Answer

1*-24 = -24
Which number added gives -2, summed -24?

4 and -6 works well

$$\large \begin{align}x^2-2x-24&=0\
x^2+4x-6x-24&=0\
x(x+4)-6(x+4)&=0\
(x-6)(x+4)&=0\
\text{Break it in two equations}\
\
(x-6)&=0 ~~~~~~~~~~~~~(1)\
x&=6
\
\
(x+4)&=0 ~~~~~~~~~~~~~(2)\
x&=-4
\end{align}$$

zepp · Answer

$$\large \begin{align} 
x^2-2x-24&=0\
\end{align}$$

$\large \text{Take the middle term's coefficient, divide by 2 and square it}$

$$\large \begin{align}
-2\div2=1;~1^2&=1\
\
x^2-2x+1&=0~ \\\text{Factorized would be}~(x-1)^2
\end{align}$$

$\large \text{Back to our question}$ 

$$\large \begin{align}
x^2-2x-24&=0\
x^2-2x&=24\ 	
x^2-2x+1&=24+1\
(x-1)^2&=25
\end{align}$$

$\large \text{Now, for what value of x this equation is true?}$

$$\large \begin{align}
(x-1)&=\pm\sqrt{25}\
x-1&=\pm 5\ 
\end{align}$$

$\large \text{Break it into two equations and solve separately.}$

$$\large \begin{align}
\
\
x-1&=5~~~~~~~~~(1)\
x&=5+1\ x&=6 \
\
x-1&=-5~~~~~~~(2)\
x&=-5+1\
x&=-4 
\end{align}$$

anonymous · Answer

thank you!

zepp · Answer

Understand the process is important :)