To solve the equation x^2-9x-15=0, would you use graphing, factoring, or completing the square if you want exact solutions? Explain.

Question

Please explain why.

(The first number is x to the power of 2)-9x-15=0

Answer 1

Graphing would not give you an exact answer, only an approximation. Factoring would be too difficult unless you use the Quadratic Formula. Therefore, I would suggest using the completing the square method to solve for "x":

x² -9x -15 original equation

(x² -9x) - 15 group what is going to be used for completing the square

To complete the square, you take the number in front of the "x" term, this case 9, and divide it by 2 to get 4.5. We put this in as a square and get

(x - 4.5)²

Using FOIL on this we get x² -9x + 20.25. In order to maintain the same original equation we must subtract 20.25.

(x² -9x + 20.25) - 15 - 20.25 = 0 maintain same equation by adding and subtracting 20.25

(x - 4.5)² -35.25 = 0 simplifying

(x - 4.5)² = 35.25 adding 35.25 to both sides

x - 4.5 = √(35.25) square root both sides

x = 4.5 ± √(35.25) add 4.5 to both sides

Therefore, the exact solutions are x = 4.5 + √(35.25) and x = 4.5 - √(35.25).

Hope this helps!

Answer 2

It doesn't seem to factor with integers, completing the square or quadratic formula seem easiest

x^2 - 9x + 81/4 - 81/4 - 15 = 0

add & subtract half of 9 squared 9/2 squared = 81/4

(x-9/2)^2 - 81/4 -60/4 = 0

(x-9/2)^2 - 141/4 = 0

(x-9/2)^2 = 141/4

x-9/2 = + or - square root of 141/4

x = 9/2 + or - sqr(141/4)

or use the quadratic formula

x = 9/2 + or - (1/2)sqr(81-4(-15) = 9/2 + or - sqr(141/4)

graphing won't give an exact solution, no matter how carefully you plot the points,

but it's a good check on your answer, as it narrows down where the zeroes are

factoring would work if factors of 15, such as 1,and 15 or 3 and 5 had a difference of 9, but they don't.

x^2 - 9x - 10 = 0 could factor since factors of 10, 1 and 10 have a difference of 9

(x-10)(x+1)