Question

homework assignment 2.5 quadratic equations
due friday by 11:59pm points 15 submitting an external tool
homework assignment 2.5 quadratic equations
score: 7/15 answered: 7/15
question 8
consider the equation: $x^{2}-4x - 96=0$
a) first, use the completing the square process to write this equation in the form $(x + d)^{2}=e$ and enter your results below.
$x^{2}-4x - 96 = 0$ is equivalent to:
preview left side of eqn:
b) solve your equation and enter your answers below as a list of numbers, separated with a comma where necessary.
answer(s):
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Explanation:

Step1: Isolate the x - terms

Given $x^{2}-4x - 96=0$, move the constant term to the right - hand side: $x^{2}-4x=96$.

Step2: Complete the square

For the quadratic expression $x^{2}-4x$, the coefficient of $x$ is $-4$. Half of it is $\frac{-4}{2}=-2$, and its square is $(-2)^{2}=4$. Add 4 to both sides of the equation: $x^{2}-4x + 4=96 + 4$.

Step3: Rewrite in the desired form

The left - hand side can be factored as a perfect square: $(x - 2)^{2}=100$.

Step4: Solve for x

Take the square root of both sides: $x-2=\pm\sqrt{100}=\pm10$.
When $x - 2 = 10$, then $x=10 + 2=12$.
When $x - 2=-10$, then $x=-10 + 2=-8$.

Answer:

A. $(x - 2)^{2}=100$
B. $12,-8$