SOLUTION: Solve. (1)x squared - 7x - 1 = 0 (2)x squared - 4x

SOLUTION: Solve. (1)x squared - 7x - 1 = 0 (2)x squared - 4x - 4 = 0 (3)6x squared = 9x

Question 122759: Solve.
(1)x squared - 7x - 1 = 0

(2)x squared - 4x - 4 = 0

(3)6x squared = 9x
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=1, b=-7, and c=-1

Negate -7 to get 7

Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because .)

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

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

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=-4, and c=-4

Negate -4 to get 4

Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because .)

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

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

# 3

Start with the given equation

Subtract 9x from both sides

Factor the left side

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answer is
or

Notice if we graph we can see that the roots are and . So this visually verifies our answer.

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