SOLUTION: Hello. Here are three problems involving the Quadratic Equation that I am having trouble with. 1. Solve the equation using factoring or the quadratic formula, whichever is ap

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello. Here are three problems involving the Quadratic Equation that I am having trouble with. 1. Solve the equation using factoring or the quadratic formula, whichever is ap      Log On


   

Question 762090: Hello. Here are three problems involving the Quadratic Equation that I am having trouble with.
1. Solve the equation using factoring or the quadratic formula, whichever is appropriate.
4/(x+6)+3/(x-6)=1
x=?
2. Solve the equation using factoring or the quadratic formula, whichever is appropriate.
1/(x+6)+1/(x+5)=1
x=?
3. Can the equation x2=11 be solved by factoring? Solve it.
x^2=11
x=?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Problem 1:
4%2F%28x%2B6%29%2B3%2F%28x-6%29=1 Multiplying both sides by (x+6)*(x-6)
4%2A%28x-6%29+%2B+3%2A%28x%2B6%29+=+%28x%2B6%29%2A%28x-6%29
4%2Ax+-+24+%2B+3%2Ax+%2B+18+=+x%5E2+-+36
x%5E2+-+7%2Ax+-+30+=+0 ---> Standard quadratic equation
Let us solve it by factoring.
x%5E2+-+10%2Ax+%2B+3%2Ax+-+30+=+0 Rewrite -7x as -10x + 3x
x%2A%28x+-+10%29+%2B+3%2A%28x+-+10%29+=+0 Take out common factor of x-10
%28x+%2B+3%29%2A%28x+-+10%29+=+0
Two solutions of the equation are x + 3 = 0 or x - 10 = 0
So roots of the equation are highlight%28x+=+-3%29 and highlight%28x+=+%2B10%29
Problem 2
1%2F%28x%2B6%29+%2B+1%2F%28x%2B5%29+=+1
Multiply both sides by (x+6)*(x+5)
x+%2B+5+%2B+x+%2B+6+=+%28x%2B5%29%2A%28x%2B6%29
2%2Ax+%2B+11+=+x%5E2+%2B+11%2Ax+%2B+30
x%5E2+%2B+9%2Ax+%2B+19+=+0
Solve using quadratic formula, as shown below. You get the 2 roots as
highlight%28x+=+-3.382%29 or highlight%28x+=+-5.618%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B9x%2B19+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%289%29%5E2-4%2A1%2A19=5.

Discriminant d=5 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+5+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+5+%29%29%2F2%5C1+=+-3.38196601125011
x%5B2%5D+=+%28-%289%29-sqrt%28+5+%29%29%2F2%5C1+=+-5.61803398874989

Quadratic expression 1x%5E2%2B9x%2B19 can be factored:
1x%5E2%2B9x%2B19+=+1%28x--3.38196601125011%29%2A%28x--5.61803398874989%29
Again, the answer is: -3.38196601125011, -5.61803398874989. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B19+%29



Problem 3:
x^2 = 11
x+=+sqrt%2811%29 or x+=+-sqrt%2811%29
:)