SOLUTION: 2x squared + 10x = -1

Question 116121: 2x squared + 10x = -1
Found 2 solutions by bucky, jim_thompson5910:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let's begin this problem by getting it into the standard quadratic form:
.

.
You can get it into the quadratic form by adding 1 to both sides of the equation to transform it
to:
.

.
By comparing this to the standard form above you can see that "a" corresponds to 2,
b corresponds to 10, and c corresponds to 1.
.
If you have trouble factoring the original problem or you suspect that the problem may have a
set of complex answers, a good method to use on a quadratic equation is the quadratic formula
which says that for the form:
.

.
the solution is given by:
.

.
for this problem, if you substitute +2 for a, +10 for b, and +1 for c, you get the solution
as:
.

.
Inside the radical sign the simplifies to . Since this is
positive you know that the two values of x will be real. The square root of 92 is 9.591663047.
Substituting this into the equation for x results in:
.

.
The -(10) is equivalent to -10 and in the denominator the 2*2 = 4. These two simplify the
equation for x to:
.

.
This means the two answers for x are:
.

.
and
.

.
Hope this helps you to do the problem. If you want to get the answers in terms of radicals,
you can replace by and your answers will be:
.

.
Which you can simplify down to:
.

.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Move all of the terms to the left side

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

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=10, and c=1

Square 10 to get 100

Multiply to get

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

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

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph , we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer

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