SOLUTION: I am stuck on 3 last questions for my practice exam and was hoping someone can show me steps to take to solve these problems. I do not expect answers, I just do not understand the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I am stuck on 3 last questions for my practice exam and was hoping someone can show me steps to take to solve these problems. I do not expect answers, I just do not understand the       Log On


   

Question 471220: I am stuck on 3 last questions for my practice exam and was hoping someone can show me steps to take to solve these problems. I do not expect answers, I just do not understand the steps to take. Please help!
Solve:
x^2+2x-4=0
b^2+3b-10=0
r^2-5r-24=0
Found 2 solutions by MathLover1, jorel1380:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Solve:..to do it, simplest way is to use quadratic formula
1.
x%5E2%2B2x-4=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...note that a=1,b=2 and c=-4

x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+

x+=+%28-2+%2B-+sqrt%28+4%2B16+%29%29%2F2+

x+=+%28-2+%2B-+sqrt%2820+%29%29%2F2+

x+=+%28-2+%2B-+4.47%29%2F2+
solutions:
x+=+%28-2+%2B4.47%29%2F2+

x+=+%282.47%29%2F2+
x+=+1.235+
or

x+=+%28-2+-4.47%29%2F2+

x+=+%28-6.47%29%2F2+
x+=+-3.235+
2.

b%5E2%2B3b-10=0
b+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-10%29+%29%29%2F%282%2A1%29+

b+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F2+
b+=+%28-3+%2B-+sqrt%2849+%29%29%2F2+
b+=+%28-3+%2B-+7%29%2F2+
solutions:
b+=+%28-3+%2B+7%29%2F2+
b+=+4%2F2+
b+=+2+
or
b+=+%28-3+-+7%29%2F2+
b+=-10%2F2+
b+=+-5+
3.

r%5E2-5r-24=0

r+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A%28-24%29+%29%29%2F%282%2A1%29+

r+=+%285+%2B-+sqrt%28+25%2B96+%29%29%2F2+

r+=+%285+%2B-+sqrt%28+121%29%29%2F2+

r+=+%285+%2B-+11%29%2F2+

solutions:

r+=+%285+%2B11%29%2F2+

r+=+16%2F2+

r+=+8+
or

r+=+%285+-11%29%2F2+

r+=+-6%2F2+

r+=+-3+



Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
x2+2x-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-4+=+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=%282%29%5E2-4%2A1%2A-4=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+1.23606797749979
x%5B2%5D+=+%28-%282%29-sqrt%28+20+%29%29%2F2%5C1+=+-3.23606797749979

Quadratic expression 1x%5E2%2B2x%2B-4 can be factored:
1x%5E2%2B2x%2B-4+=+1%28x-1.23606797749979%29%2A%28x--3.23606797749979%29
Again, the answer is: 1.23606797749979, -3.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-4+%29

--------------
b2+3b-10=0
(b+5)(b-2)=0
b=-5 or 2
------------
r2-5r-24=0
(r-8)(r+3)=0
r=8 or -3..