SOLUTION: Use the quadratic formula to solve the following equation for x, show as much work as possible: 0 = 2x2 - 5x - 18.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use the quadratic formula to solve the following equation for x, show as much work as possible: 0 = 2x2 - 5x - 18.       Log On


   

Question 410986: Use the quadratic formula to solve the following equation for x, show as much work as possible: 0 = 2x2 - 5x - 18.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Please use the "^" symbol (SHIFT+6) to indicate exponents. "2x2" could be interpreted as 2 times x times 2.

The general quadratic equation is:
ax%5E2+%2B+bx+%2B+c+=+0
You must learn this because the Quadratic Formula:
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a
is written in terms of the a, b and c from the genreal equation.

With your equation
0+=+2x%5E2+-+5x+-+18
a = 2
b = -5
c = -18
(If you don't see why b and c are negative, then look at the general equation. It is written with additions. So you have to write (ar least think of) your equation with additions: 0+=+2x%5E2+%2B+%28-5x%29+%2B+%28-18%29

Now we just substitute these values into the formula and simplify:
x+=+-%28-5%29+%2B-+sqrt%28%28-5%29%5E2+-+4%282%29%28-18%29%29%29%2F2%282%29
which simplifies as follows:
x+=+%28-%28-5%29+%2B-+sqrt%2825+-+4%282%29%28-18%29%29%29%2F2%282%29
x+=+%28-%28-5%29+%2B-+sqrt%2825+%2B+144%29%29%2F2%282%29
x+=+%28-%28-5%29+%2B-+sqrt%28169%29%29%2F2%282%29
x+=+%285+%2B-+sqrt%28169%29%29%2F4
x+=+%285+%2B-+13%29%2F4
Quadratic equations have two solutions. The "plus or minus" symbol in the formula is a shorthand way of expressing both solutions within the same expression. It is now time to write the two solutions separately. This last expression is a shorthand way of saying:
x+=+%285+%2B+13%29%2F4 or x+=+%285+-+13%29%2F4
We can now continue with the simplifying:
x+=+18%2F4 or x+=+%28-8%29%2F4
x+=+9%2F2 or x+=+-2