Please help me!! it's due soon! I'll mark you BRAINLIEST if you answer right. Fill in the blanks.

Mathematics

2 answers:

34kurt3 years ago

6 0

Answer:

$(x-2)^2=36$

Step-by-step explanation:

In order to figure out what number should go in the blank within the parentheses, we use the formula $\frac{b}{2}$ , where b is the coefficient of the x term. In this case, b = -4. So, the number in the parentheses blank is: $\frac{-4}{2} =-2$ .

Now, on the left, our parenthetical expression is: $(x-2)^2$ . However, we're not done. The top and bottom equations still need to equal each other. Let's see if they are equal by expanding the $(x-2)^2$ : $(x-2)^2=x^2-4x+4$ . Clearly, they're not the same because the top equation has a -32, whereas the bottom one has +4. So, in order to make these the same, we need to add or subtract something to the right side of the bottom equation.

What will make the left side have -32? If the right side has + 36: $x^2-4x+4=36$ . We can check this by subtracting 36 from both sides: $x^2-4x+4-36=36-36$ ⇒ $x^2-4x-32=0$ ... and they match.