1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ksenya-84 [330]
2 years ago
15

What are the solutions to the quadratic equation below x^2+20x+100=7​

Mathematics
1 answer:
aleksandrvk [35]2 years ago
7 0

First you must have the quadratic equal to zero. In order to do this you must subtract 7 to both sides

x^2 + 20x + (100 - 7) = 7 - 7

x^2 + 20x + 93 = 0

Now you must find two numbers who's sum equals 20 and their multiplication equal 93

Are there any? NO!

This means that you have to use the formula:

\frac{-b±\sqrt{b^{2} - 4ac} }{2a}

In this case:

a = 1

b = 20

c = 93

\frac{-(20) plus/minus\sqrt{20^{2} - 4(1)(93)} }{2*1}

\frac{-20 plus/minus\sqrt{400 - 372} }{2}

\frac{-20 plus/minus\sqrt{28} }{2}

^^^We must simplify √28

√28 = 2√7

so...

\frac{-20 plus/minus 2\sqrt{7} }{2}

simplify further:

-10 plus/minus\sqrt{7

-10 + √7

or

-10 - √7

***plus/minus = ±

Hope this helped!

~Just a girl in love with Shawn Mendes

You might be interested in
HELP ME PLEASE WITH 1,2 AND 3 PLEASE DON'T TAKE LONG TO RESPOND !!​
soldi70 [24.7K]

Answer:

1. -19x

3. 23 -  8x

5. -18x + 2y

Step-by-step explanation:

first: 3x - x = 2x

2x - 22x = -20x

-20x + x = -19x

second one:

8 - (-15) = 23

12x - 20x = -8 x

23 - 8x

third:

-10x - 8x = -18x

3y - y = 2y

-18x + 2y

6 0
2 years ago
Read 2 more answers
A soccer ball is kicked from 3 feet above the ground. the height,h, in feet of the ball after t seconds is given by the function
dexar [7]
Here's our equation.

h=-16t+64t+3

We want to find out when it returns to ground level (h = 0)

To find this out, we can plug in 0 and solve for t.

0 = -16t+64t+3 \\ 16t-64t-3=0 \\ use\ the\ quadratic\ formula\ \frac{-b\±\sqrt{b^2-4ac}}{2a}  \\ \frac{-(-64)\±\sqrt{(-64)^2-4(16)(-3)}}{2*16}  = \frac{64\±\sqrt{4096+192}}{32}

= \frac{64\±\sqrt{4288}}{32} = \frac{64\±8\sqrt{67}}{32} = \frac{8\±\sqrt{67}}{4} = \boxed{\frac{8+\sqrt{67}}{4}\ or\ 2-\frac{\sqrt{67}}{4}}

So the ball will return to the ground at the positive value of \boxed{\frac{8+\sqrt{67}}{4}} seconds.

What about the vertex? Simple! Since all parabolas are symmetrical, we can just take the average between our two answers from above to find t at the vertex and then plug it in to find h!

\frac{1}2(\frac{8+\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(2+\frac{\sqrt{67}}{4}+2-\frac{\sqrt{67}}{4}) = \frac{1}2(4) = 2

h=-16t^2+64t+3 \\ h=-16(2)^2+64(2)+3 \\ \boxed{h=67}


8 0
3 years ago
A train is traveling at a constant speed and goes a distance of 7 1/2 kilometers in 6 minutes the train will continue at this sp
Alla [95]

Answer:

392939939393939399393939393

Step-by-step explanation:

7 0
3 years ago
How many 1-centimeter squares fit along the length of the rectangle
Damm [24]
It would depend on how large the rectangle is
4 0
2 years ago
Calculate pt3 such that a line from pt1 to pt3 is perpendicular to the line from pt1 to pt2, and the distance between pt1 and pt
Leni [432]
Let the point_1 = p₁ = (1,4)
and      point_2 = p₂ = (-2,1)
and      Point_3 = p₃ = (x,y)

The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)

The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d = \sqrt{Δx^2+Δy^2}
d₁ = \sqrt{(-2-1)^2+(1-4)^2}
d₂ = \sqrt{(x-1)^2+(y-4)^2}
d₁ = d₂
∴ \sqrt{(-2-1)^2+(1-4)^2} = \sqrt{(x-1)^2+(y-4)^2} ⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
 (x-1)²+(y-4)² = 18
from equatoin (1)  y-4 = 1-x
∴(x-1)²+(1-x)² = 18            ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 = \pm \sqrt{9} = \pm 3
∴ x = 4 or x = -2
∴ y = 1 or y = 7

Point_3 = (4,1)  or  (-2,7)












8 0
3 years ago
Other questions:
  • as a favor to her friend, Natasha worked 7 hours at a diner for $10 per hour last week. she also makes $8 per hour when she baby
    14·2 answers
  • Jose bought 750 bags of peanuts for $375.00. He intends to sell each bag for $0.15 more than he paid. How much should he charge
    5·1 answer
  • Commutative vs associative property
    9·1 answer
  • How many hours must you run if you want to run 27 km at a rate of 9 km/h? (Apex)
    9·1 answer
  • How do you round 0.955 to the nearest tenth
    15·2 answers
  • Factor the expression completely.<br> 18X2-8
    8·2 answers
  • Sales-Related and Purchase-Related Transactions Using Perpetual Inventory System
    10·1 answer
  • PLS HELP ME I NEED THIS FAST PLS DONT JUST SEND LINKS... I NEED HELP PLS
    6·1 answer
  • Find the value of x and y <br> (5y-23) <br> (2x+13)<br> (3x)<br> 47
    15·1 answer
  • I need help comparing the two added pictures below, thx ;)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!