All categories

3 years ago

Solve the equation for x. x2 = 36 The solutions to the equation are and

Mathematics

2 answers:

andrey2020 [161]3 years ago

3 0

x2=36

We move all terms to the left:

x2-(36)=0

We add all the numbers together, and all the variables

x^2-36=0

a = 1; b = 0; c = -36;

Δ = b2-4ac

Δ = 02-4·1·(-36)

Δ = 144

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

x1=−b−Δ√2ax2=−b+Δ√2a

Δ‾‾√=144‾‾‾‾√=12

x1=−b−Δ√2a=−(0)−122∗1=−122=−6

x2=−b+Δ√2a=−(0)+122∗1=122=6

bekas [8.4K]3 years ago

3 0

9514 1404 393

Answer:

x = -6 or +6

Step-by-step explanation:

You know from your multiplication tables that 6×6 = 36, so one answer is ...

x = 6

You also know that the product of two negative numbers is positive, so another answer is ...

x = -6

Check

x² = 6² = 6×6 = 36

x² = (-6)² = (-6)×(-6) = 36

_____

Alternate approach

If you like, you can rewrite the equation as ...

x² -36 = 0

This can be factored to ...

(x -6)(x +6) = 0

The zero product rule tells you this product will only be zero if one or the other factors is zero.

x -6 = 0 ⇒ x = 6

x +6 = 0 ⇒ x = -6

The two solutions are x = ±6.

You might be interested in

What is 60 x 473 I'm so confused pls help :(

Anestetic [448]

Answer:

28,389

Step-by-step explanation:

8 0

3 years ago

9 more than 4 times the square of a number.

musickatia [10]

Answer:

4n+9

hope this helps

have a good day :)

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Mr wellborn arrives at work at 8:40 a.m he leaves for work 50 minutes before he arrives at what time does Mr wellborn leave for

Yuri [45]

Mr Wellborn arrives at work at 7:50 am. If you take 60 minutes away from 8:40 its 7:40 but take away 10 minutes and its 7:50.

8 0

3 years ago

Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

Step-by-step explanation:

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

Step-by-step explanation:

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

Step-by-step explanation:

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

6 0

3 years ago

Find the square root of 13²

nadezda [96]

The answer to that would be “169”

3 0

3 years ago