All categories

3 years ago

What equation results from completing the square and then factoring? x2 + 10X = 15

Mathematics

1 answer:

Mandarinka [93]3 years ago

3 0

Answer:

C) (x + 5)² = 40

Step-by-step explanation:

Given the quadratic equation, x² + 10x = 15:

To complete the square, take the coefficient of the middle term (b), and divide it by 2a:

x² + 10x + $[\frac{b}{2a}]^{2}$ = 15 + $[\frac{b}{2a}]^{2}$

x² + 10x + $[\frac{10}{2}]^{2}$ = 15 + $[\frac{10}{2}]^{2}$

x² + 10x + 5² = 15 + 5²

x² + 10x + 25 = 40

The trinomial on the left-hand side of the equation provides a perfect square binomial factors: u² + 2uv + v² = (u + v)²

x² + 10x + 25 = 40

(x + 5)² = 40

Therefore, the correct answer is Option C) (x + 5)² = 40

You might be interested in

What is 1-2sin^2x=sinx Please show steps and find all solutions in interval [0,2pi)

Svetlanka [38]

Answer:

$\large\boxed{x=\dfrac{3\pi}{2}\ \vee\ x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}$

Step-by-step explanation:

$1-2\sin^2x=\sin x\\\\\text{substitute}\ t=\sin x,\ t\in[-1,\ 1]\\\\1-2t^2=t\qquad\text{subtract t from both sides}\\\\-2t^2-t+1=0\qquad\text{change the signs}\\\\2t^2+t-1=0\\\\2t^2+2t-t-1=0\\\\2t(t+1)-1(t+1)=0\\\\(t+1)(2t-1)=0\iff t+1=0\ \vee\ 2t-1=0\\\\t+1=0\qquad\text{subtract 1 from both sides}\\\boxed{t=-1}\\\\2t-1=0\qquad\text{add 1 to both sides}\\2t=1\qquad\text{divide both sides by 2}\\\boxed{t=\dfrac{1}{2}}$

$\sin x=-1\to x=-\dfrac{\pi}{2}+2k\pi,\ k\in\mathbb{Z}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}\\\\x\in[0,\ 2\pi)$

$x=-\dfrac{\pi}{2}\notin[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+2\pi=\dfrac{3\pi}{2}\in[0,\ 2\pi)\\\\x=-\dfrac{\pi}{2}+4\pi=\dfrac{7\pi}{2}\notin[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{\pi}{6}+2\pi=\dfrac{13\pi}{6}\notin[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}\in[0,\ 2\pi)\\\\x=\dfrac{5\pi}{6}+2\pi=\dfrac{17\pi}{6}\notin[0,\ 2\pi)$

4 0

4 years ago

The ratio of boys to girls in 8th grade at ESHS is 5:3. Calculate the number of boys if there are 210 girls. What is the total n

frosja888 [35]

Answer:

350

Step-by-step explanation:

If there are 210 girls, then the number of boys is (210÷3)x7=350.

5 0

3 years ago

Read 2 more answers

Khan academy literally rejected my correct answer in all fraction form and I changed only the y-intercept to the decimal equival

skad [1K]

Y=-2x+-3 I haven't't done this in a long time, sorry. I do remember wanting to k**l myself because this always happened to me when I did remember this stuff

7 0

4 years ago

I dont know how to do this.

Aleksandr-060686 [28]

The answer to the question

5 0

3 years ago

How many terms are in the expression? 9a + 6b + 3c + 1 A) 1 B) 2 C) 3 D) 4

Kaylis [27]

Answer:

D.) there is 9a and 6b ,3c and 1 thats four different terms

Step-by-step explanation:

Have a nice day! :D

7 0

2 years ago