Question

Y=2x^2-2x+1 and y=3x-5

Answer 1

3.4 or - 0.9

Explanation:

y =3x-5

Also, y = 2x^2 - 2x + 1

Let's equate the two values of y

3x - 5 = 2x^2 - 2x + 1

Collect like terms

-5 - 1 = 2x^2 - 2x - 3x

-6 = 2x^2 - 5x

Take -6 to the other side to become + 6 and equate to zero to form a quadratic equation

2x^2 - 5x + 6 = 0

Now, let's think of two numbers that when multiplied give 2 * 6 = 12, and when summed give -5

oh ooh! it seems like those numbers are impossible to find

Have no fear, we can use an alternative method to solve for x. We'll use the quadratic formula!

-b +/-
`√(b^2) + 4ac` / 2a

where a = 2

b = -5

c = 6

Let's insert these values in the quadratic formula

- (-5) +/-
`√(-5^2) + 4*(2*6)` / 2(2)

5 +/-
`√(25) + 48` /4

= 5+/-
`√(73)` /4

= 5+/- 8.54 /4

= 5 + 8.54 / 4 OR = 5 - 8.54 /4

= 13. 54 /4 = -3.54 /4

= 3.385 = - 0.885

rounding up to one decimal place

Therefore, x is 3.4 or - 0.9