SOLUTION: Hello to all,I need some help with some problems.The first one is,Use the quadratic formula to solve:x^2+8x+7=0.The next one is,Use the quadratic formula to solve:x^2+12x+11=0.The

Question 92399: Hello to all,I need some help with some problems.The first one is,Use the quadratic formula to solve:x^2+8x+7=0.The next one is,Use the quadratic formula to solve:x^2+12x+11=0.The next one is,Use the quadratic formula to solve:5x^2+12=-6x.And the last one is,Find the y-intercept of y=2^x.Thanks to whoever can help.
Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X^2+8X+7=0
X=(-8+-SQRT[8^2-4*1*7])/2*1
X=(-8+-SQRT[64-28])/2
X=(-8+-SQRT[36])/2
X=(-8+-6)/2
X=(-8+6)/2
X=-2/2
X=-1 ANSWER.
X=(-8-6)/2
X=-14/2
X=-7 ANSWER.
I DID THE FIRST TO SHOW YOU HOW IT IS DONE, NOW YOU FINISH THE REST OF THEM.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"Use the quadratic formula to solve:x^2+8x+7=0."

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=8, and c=7

Square 8 to get 64

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

"Use the quadratic formula to solve:x^2+12x+11=0"

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=12, and c=11

Square 12 to get 144

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

"Use the quadratic formula to solve:5x^2+12=-6x"

Add 6x to both sides

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=5, b=6, and c=12

Square 6 to get 36

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 5 to get 10

After simplifying, the quadratic has roots of

or

Notice if we graph the quadratic , we get

graph of
And we can see that there are no real roots

To visually verify the answer, check out this page to see a visual representation of imaginary roots

"Find the y-intercept of y=2^x"

To find the y-intercept, simply plug in x=0

plug in x=0

Evaluate the exponent

So the y-intercept is (0,1)
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