Solve the equation using a method other than factoring. Show all your work. x² - 7x + 3 = 0

1 answer:

5 0

Completing the square

7/2=3.5
3.5^2=12.25
add that to both sides
x²-7x+12.25+3=12.25
factor perfect square
(x-3.5)²+3=12.25
minus 3 both sides
(x-3.5)²=9.25
square root both sides
x-3.5=+/-√9.25
add 3.5 to both sides
x=3.5+/-√9.25

x=3.5+√9.25 or 3.5-√9.25

You might be interested in

Indicate the equation of the given line in standard form.

Ganezh [65]

Since the slope stays the same as it's parallel, we have y=(3/4)x+b. Plugging (2,-1) in, we get -1=3*2/4+b=6/4+b=1.5+b. Subtracting 1.5 from both sides, we get -2.5=b and our equation being y=(3/4)x-2.5 (since in y=mx+b, y and x remain as variables)

8 0

3 years ago

[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?

Nitella [24]

Answer:

Step-by-step explanation:

Given the logarithmic equation

$\log_4x+\log_4(x-3)=\log_4(-7x+21)$

First, notice that

$x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x$

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

$\log_4x+\log_4(x-3)=\log_4x(x-3),$

then

$\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3$

Hence, $x=3$ and $x=-7$ are extraneous solutions

6 0

3 years ago

suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50. how mush does each mango and each apple co

Zanzabum

Suppose a mango cost x dollar and a apple cost y dollar

there will be an binary system of equation

8*x+3*y=18
3*x+5*y=14.5

so soultions have to x=48/31 y=16/31

6 0

3 years ago

Read 2 more answers

Of the 10 people attending a seminar, 2 have red hair.

kari74 [83]

Answer:

20%

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A 90% confidence interval for the mean height of students