SOLUTION: Solve using the quadratic formula: x2 � 3x � 23 = 5

Question 113753: Solve using the quadratic formula:
x2 � 3x � 23 = 5

Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X^2-3X-23=5
X^2-3X-23-5=0
X^2-3X-28=0

X=(3+-SQRT[(3^2-4*1*-28])/281
X=(3+-SQRT9+112)/2
X=(3+-SQRT121)/2
X=(3+-11)/2
X=(3+11)/2
X=14/2
X=7 ANSWER.
X=(3-11)/2
X=-8/2
X=-4 ANSWER.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract 5 from both sides

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=-3, and c=-28

Negate -3 to get 3

Square -3 to get 9 (note: remember when you square -3, 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

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

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