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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
X^2+8X+7=0 x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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) About Me  (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

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2%2B8%2Ax%2B7=0 ( notice a=1, b=8, and c=7)

x+=+%28-8+%2B-+sqrt%28+%288%29%5E2-4%2A1%2A7+%29%29%2F%282%2A1%29 Plug in a=1, b=8, and c=7



x+=+%28-8+%2B-+sqrt%28+64-4%2A1%2A7+%29%29%2F%282%2A1%29 Square 8 to get 64



x+=+%28-8+%2B-+sqrt%28+64%2B-28+%29%29%2F%282%2A1%29 Multiply -4%2A7%2A1 to get -28



x+=+%28-8+%2B-+sqrt%28+36+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-8+%2B-+6%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-8+%2B-+6%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-8+%2B+6%29%2F2 or x+=+%28-8+-+6%29%2F2

Lets look at the first part:

x=%28-8+%2B+6%29%2F2

x=-2%2F2 Add the terms in the numerator
x=-1 Divide

So one answer is
x=-1



Now lets look at the second part:

x=%28-8+-+6%29%2F2

x=-14%2F2 Subtract the terms in the numerator
x=-7 Divide

So another answer is
x=-7

So our solutions are:
x=-1 or x=-7

Notice when we graph x%5E2%2B8%2Ax%2B7, we get:

+graph%28+500%2C+500%2C+-17%2C+9%2C+-17%2C+9%2C1%2Ax%5E2%2B8%2Ax%2B7%29+

and we can see that the roots are x=-1 and x=-7. 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

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2%2B12%2Ax%2B11=0 ( notice a=1, b=12, and c=11)

x+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A1%2A11+%29%29%2F%282%2A1%29 Plug in a=1, b=12, and c=11



x+=+%28-12+%2B-+sqrt%28+144-4%2A1%2A11+%29%29%2F%282%2A1%29 Square 12 to get 144



x+=+%28-12+%2B-+sqrt%28+144%2B-44+%29%29%2F%282%2A1%29 Multiply -4%2A11%2A1 to get -44



x+=+%28-12+%2B-+sqrt%28+100+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-12+%2B-+10%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-12+%2B-+10%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-12+%2B+10%29%2F2 or x+=+%28-12+-+10%29%2F2

Lets look at the first part:

x=%28-12+%2B+10%29%2F2

x=-2%2F2 Add the terms in the numerator
x=-1 Divide

So one answer is
x=-1



Now lets look at the second part:

x=%28-12+-+10%29%2F2

x=-22%2F2 Subtract the terms in the numerator
x=-11 Divide

So another answer is
x=-11

So our solutions are:
x=-1 or x=-11

Notice when we graph x%5E2%2B12%2Ax%2B11, we get:

+graph%28+500%2C+500%2C+-21%2C+9%2C+-21%2C+9%2C1%2Ax%5E2%2B12%2Ax%2B11%29+

and we can see that the roots are x=-1 and x=-11. This verifies our answer



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

5x%5E2%2B6x%2B12=0 Add 6x to both sides

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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 5%2Ax%5E2%2B6%2Ax%2B12=0 ( notice a=5, b=6, and c=12)

x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A5%2A12+%29%29%2F%282%2A5%29 Plug in a=5, b=6, and c=12



x+=+%28-6+%2B-+sqrt%28+36-4%2A5%2A12+%29%29%2F%282%2A5%29 Square 6 to get 36



x+=+%28-6+%2B-+sqrt%28+36%2B-240+%29%29%2F%282%2A5%29 Multiply -4%2A12%2A5 to get -240



x+=+%28-6+%2B-+sqrt%28+-204+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+2%2Ai%2Asqrt%2851%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-6+%2B-+2%2Ai%2Asqrt%2851%29%29%2F%2810%29 Multiply 2 and 5 to get 10



After simplifying, the quadratic has roots of

x=-3%2F5+%2B+sqrt%2851%29%2F5%2Ai or x=-3%2F5+-+sqrt%2851%29%2F5%2Ai

Notice if we graph the quadratic y=5%2Ax%5E2%2B6%2Ax%2B12, we get

+graph%28+500%2C+500%2C+-15.6%2C+14.4%2C+-4.8%2C+25.2%2C+5%2Ax%5E2%2B6%2Ax%2B12%29+ graph of y=5%2Ax%5E2%2B6%2Ax%2B12
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


y=2%5E0 plug in x=0

y=1 Evaluate the exponent

So the y-intercept is (0,1)