What is the value of x? <br><br> Enter your answer in the box. <br><br> X =

Which quadratic equation is equivalent to (x - 4)2 – ( - 4) - 6 = 0?

zmey [24]

Answer:

$u^2-u-6=0$

where

$u=(x-4)$

Step-by-step explanation:

we have

$(x-4)^2-(x-4)-6=0$

Let

$u=(x-4)$

substitute in the expression above

$(u)^2-(u)-6=0$

Solve for u

Complete the square

$(u^2-u+0.25)=6+0.25$

$(u^2-u+0.25)=6.25$

Rewrite as perfect squares

$(u-0.5)^2=6.25$

square root booth sides

$u-0.5=\pm2.5$

$u=0.5\pm2.5$

$u_1=0.5+2.5=3$

$u_2=0.5-2.5=-2$

Solve for x

Remember that

$u=(x-4)$

For u=3

$3=(x-4)$ ----> $x=7$

For u=-2

$-2=(x-4)$ ----> $x=2$

7 0

3 years ago

Find two positive numbers whose difference is 30 and whose product is 2584.

kvasek [131]

Answer:

$38$ and $68$ .

Step-by-step explanation:

Let $x$ be the smaller one of the two number.

$x$ must be a positive integer. The other number would be $(x + 30)$ .

The question states that the product of the two numbers is $2584$ . In other words:

$x\, (x + 30) = 2584$ .

Rearrange this equation and solve for $x$ :

$x^{2} + 30\, x - 2584 = 0$ .

The first root of this quadratic equation would be:

$\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}$ .

Similarly, the second root of this quadratic equation would be:

$\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}$ .

Since the question requires that both numbers should be positive, $x > 0$ . Therefore, only $x = 38$ is valid.

Hence, the two numbers would be $38$ and $(38 + 30)$ , which is $68$ .

6 0

3 years ago

Read 2 more answers

Help pleaseee ASAP ASAP

Yanka [14]

Answer:

I think the answer is the third one

Step-by-step explanation:

7 0

3 years ago

(4x+3)(3x)-25 graph

maw [93]

Answer:

12x^2+9x^2-25 (quadratic equation)

a=12, b=9, c=-25

put this in quadratic formula

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the mean of the data set?

svetoff [14.1K]

B) 12.75
Just add them all together
10+15+14+8+18+11+12+12+10+10+17+16=153
The devide the anser by the ammount of numbers you added together
153÷12=12.75

8 0

3 years ago

Read 2 more answers

What is the value of x? Enter your answer in the box. X =