SOLUTION: Good evening, I'm having trouble finding the x-intercept of the following equation: {{{2x^2+16x+9}}} I already managed to complete the square to get the vertex form: {{{2(

Question 367314: Good evening, I'm having trouble finding the x-intercept of the following equation:

I already managed to complete the square to get the vertex form:

The y-intercept is 9, obtained by plugging 0 in for x and solving for y.
The vertex is (4, -23), but I don't understand how to find the x-intercept. I graphed the equation and the x-intercepts are somewhere around (-7.5, 0) and (-0.6, 0) but I have no idea how to calculate these. Please help! Your time is much, MUCH appreciated :)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There are two ways to do this. Both methods involve setting each expression equal to zero.

Method 1:

Start with the given equation.

Notice that the quadratic is in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

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

or Break up the expression.

or Reduce.

So the solutions are or

This means that the x-intercepts are

and

======================================================================

Method 2:

Start with the given equation.

Add to both sides.

Combine like terms.

Divide both sides by .

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Simplify the square root.

or Subtract from both sides.

or Combine the fractions.

--------------------------------------

Answer:

So the solutions are or .

So again, the x-intercepts are

and

Note: The approximate form of the x-intercepts is x-intercepts are

and

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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