SOLUTION: xsquared-13x=-10

Start with the given equation

x%5E2-13x%2B10=0

Add 10 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 x%5E2-13%2Ax%2B10=0

( notice

, and

)

Plug in a=1, b=-13, and c=10

x+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29

Negate -13 to get 13

x+=+%2813+%2B-+sqrt%28+169-4%2A1%2A10+%29%29%2F%282%2A1%29

Square -13 to get 169 (note: remember when you square -13, you must square the negative as well. This is because %28-13%29%5E2=-13%2A-13=169

Multiply

to get

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

x+=+%2813+%2B-+sqrt%28129%29%29%2F%282%2A1%29

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

x+=+%2813+%2B-+sqrt%28129%29%29%2F2

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%2813+%2B+sqrt%28129%29%29%2F2

Now break up the fraction

x=%2B13%2F2%2Bsqrt%28129%29%2F2

Simplify

So these expressions approximate to

x=12.1789083458003

So our solutions are:
x=12.1789083458003

Notice when we graph x%5E2-13%2Ax%2B10

, we get:

when we use the root finder feature on a calculator, we find that x=12.1789083458003

and

.So this verifies our answer