Question

How do you solve this math problem?
2x²-29x+90

Answer 1

2x² - 29x + 90 = 0

You can solve this problem in different ways, but for the purpose of this explanation I will solve and explain using the quadratic formula

Use the quadratic equation to solve this (image of the quadratic equation is below)

Remember that quadratic functions are set up like so:

$ax^{2} +bx +c = 0$

That means that in this equation...

a = 2

b = -29

c = 90

^^^Plug these numbers into the quadratic equation and solve

$\frac{29\pm\sqrt{(-29)^{2}-4(2)(90)}}{2(2)}$

$\frac{29\pm\sqrt{841-720}}{4}$

$\frac{29\pm\sqrt{121}}{4}$

$\frac{29\pm11}{4}$

This expression will have TWO answers

$\frac{29+11}{4}$ ---> $\frac{40}{4}$ ---> 10

$\frac{29-11}{4}$ ---> $\frac{18}{4}$ ---> $\frac{9}{2}$ OR 4.5

Check:

2(10)²- 29(10) + 90 = 0 ---> 2(100) - 290 + 90 = 0 ---> 200 - 290 + 90 = 0 ---> -90 + 90 = 0 ---> 0 = 0

2(4.5)²- 29(4.5) + 90 = 0 ---> 2(20.25) - 130.5 + 90 = 0 ---> 40.5 - 130.5 + 90 = 0 ---> -90 + 90 = 0 ---> 0 = 0

A factor is structured like so:

(x - a)(x - b)

The answers solved above will go in the a and b spots respectively:

(x - 10)(x -  $\frac{9}{2}$) ---> (x - 10)(2x - 9)

Hope this helped!

~Just a girl in love with Shawn Mendes