Search 74,174 tutors
1 0

# 5x^2 + 8x -69=0

5x^2+ 8x -69=0 solve by factoring

5x^2 + 8x - 69 = (5x+23)(x-3) = 0

x = -23/5, 3

Ideas: 5*(-69) = 23*(-15), and 23-15 = 8, the coefficient of x.

So, 5x^2 + 8x -69 = 5x^2-15x + 23x-69 = 5x(x-3) + 23(x-3) = (5x+23)(x-3)

5X^2 + 8X -69 =0

Have to find out 2 numbers whose Sum is 8   and product is  5* 69 =- 345

first write 345 as product of its prime factor, by doing division 3

345 = 3 * 5 * 23  , find 2 factors whose difference is - 8,  15&23.

Break 8x into 2 parts 23, 15

5 X2 - 15X + 23X - 69 =0
Now we factor by Grouping
5X( X -3) +23( X -3 )  = ( X - 3 ) ( 5X + 23)

Hey Rachel -- the final figure "-69" suggests a "multiple-of-3-type" factor ... 5*3*3 +8*3 -69= 45 +24 -69 =0 works ... (x-3) factor leaves the (5x +23) element ==> x= -23/5, 3 ... Best wishes, ma'am :)

(5x  + 23)(x  - 3)

Hi Rachel. I will solve a similar problem, via a method called group factoring. Then, I will show how this relates to solving your problem. Note first that this equation has the form, a*x^2 + b*x + c = 0. For example, 3x^2 - 17x - 56 = 0.

Solution Steps.

Step 1: multiply a by c. Here, we have that 3*( -56) = -168.

Step 2: Find two factors of the product in step 1 that will multiply  to give that same product and add to give b, that is, -17 in his example (see the original example above). Note that -24*7 = -168, and -24 + 7  = -17, as desired.

Step 3: Note that the factors in step 2 pertain to the coefficient of x in the originalequation. So now, rewrite bx as a sum, using the factors that we just got in step 2. Here, we rewrite -17x as -24x +7x. Now, rewrite the whole equasuit using this new replacement. We get the equation 3x^2 -24x +7x -56 = 0.

Step 4: factor the last equation, from step 3 by splitting it into two groups and factoring each group completely as follows, on the left side of the equation. We do this as follows:

3x^2 - 24x + 7x - 56 = 0 becomes

3x(x-8)+7(x-8)=0, where we note that (x-8) is common to both the left sum and the right summand, and so we can factor out the (x -8) to get the equation

(x-8)(3x+7)=0 which tells uat that x -8 =0, whence x=8, and/or 3x+7=0 whence 3x =-7 whence x = -7/3.

I will now start you out with your problem which you can use my the above steps to complete...

Step1: Multiply  5 by -69 to get -345.

Step 2: Here we see that the useful factors of -345 are -23 and 15, since -23 *15 = -345, and -23 + 15  = 8, as required.

Now, you can finish the problem, using the steps in my guided example.

All the best!