Answer:
3.4 or - 0.9
Step-by-step 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 +/- [tex]\sqrt{b^2} + 4ac[/tex] / 2a
where a = 2
b = -5
c = 6
Let's insert these values in the quadratic formula
- (-5) +/- [tex]\sqrt{-5^2} + 4*(2*6)[/tex] / 2(2)
5 +/- [tex]\sqrt{25} + 48[/tex] /4
= 5+/- [tex]\sqrt{73}[/tex] /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
