# `y = -0.1x^2 + 3.2x - 3.5` find the x-intercepts by factoring.

hkj1385 | Certified Educator

To find the x-intercepts, 'y' must be equal to zero

i.e., -0.1*(x^2) + 3.2x - 3.5 = 0

Multiplying both sides by 10, we get

or, -(x^2) + 32x - 35 = 0

Multiplying both sides by -1, we get

or, (x^2) - 32x + 35 = 0

or, {(x^2) - 2*(1*16*x) + (16^2)} - 231 = 0

or, {(x-16)^2} - 231 = 0

or, {(x-16)^2} = 231

or, (x-16) = +sqrt(231)  or - sqrt(231)

or, x = [16 + sqrt(231)] or [16 - sqrt(231)]

Thus, the x-intercepts are [16 + sqrt(231)] or [16 - sqrt(231)]

jasminehems | Student

Is this a trick question?  I tried every factoring I could find of 3.5 and .1, but none of them would give me 3.2 when I FOILed to check my answer.  I resorted to using the Quadratic Formula, and I found that the solutions are irrational numbers.  If the solutions are irrational, then this problem cannot be solved by factoring.

I see. Can the x-intercepts be found any other way.

For any Quadratic, whether it is factorable or not, you can find the exact zeros by using the Quadratic Formula:

`-b+-sqrt(b^2-4(a)(c))/(2(a))`

`y=ax^2+bx+c`

oldnick | Student

`y=-0.1x^2+3.2x-3.5`

we can rwrite y so:

`y=-1/10(x^2-32x+35)`

so  `y=0 rArr` `x^2-32x+35=0`

`x^2-32x+256+35= 256`

`(x-16)^2=256-35`

`(x-16)^2=221`

`x-16=+-sqrt(221)`

`x=16+-sqrt(221)`

are the solutions required:  `x_1=30.86606875`  `x_2=1.13393125`