SOLUTION: Use the quadratic formula to solve the equation. -2x^2+x+8=0 Solve the equation. x^2+18x+81=25 Simplify (square root of -175) using the imaginary number i.

Question 119411: Use the quadratic formula to solve the equation.
-2x^2+x+8=0
Solve the equation.
x^2+18x+81=25
Simplify (square root of -175) using the imaginary number i.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

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=1, and c=8

Square 1 to get 1

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

#2

Start with the given equation

Subtract 25 from both sides

Combine like terms

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=1, b=18, and c=56

Square 18 to get 324

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 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

Solved by pluggable solver: Simplifying Square Roots (whole numbers only)

Start with the given expression

Factor out a negative 1

Break up the square roots using the identity

Replace with (remember )

Now lets simplify :

The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.

So let's list the factors of 175

Factors:

1, 5, 7, 25, 35, 175

Notice how 25 is the largest perfect square, so lets factor 175 into 25*7

Factor 175 into 25*7

Break up the square roots using the identity

Take the square root of the perfect square 25 to get 5

So the expression simplifies to

---------------------
Answer:

So the expression

simplifies to

(just reintroduce back in)

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