How do you solve 2x ^ { 2} + 57x = 497?
2 Answers
Explanation:
First we must convert our initial equation so that it fits satisfies
2x^2 + 57x = 497 becomes2x^2 + 57x - 497 = 0 .
From here we conclude the following:
a=2
b=57
c=-497
Now we use the quadratic formula to find the value of
x = (-b +- sqrt(b^2 -4ac))/(2a)
x = (-57 +- sqrt(57^2 -4(2)(-497)))/(2(2))
x = (-57 +- sqrt(3249 -8(-497)))/(4)
x = (-57 +- sqrt(3249 + 3976))/(4)
x = (-57 +- sqrt(7225))/(4)
x = (-57 +- 85)/(4)
x = (-57 + 85)/4 ,x=(-57-85)/4
x = (28)/(4) ,x = (-142)/(4)
x = 7 ,x=-35.5
In this case it is not specified whether we want the positive
Given:
We can quickly turn this into an easily recognizable quadratic equation by subtracting 497 from both sides to get:
There are a couple of "give aways" we can see on this equation that will take us to the solution:
1) The
2) the multiplier
Setting up the brackets:
There is a
Then:
And:
To check, put the answers back into the
And the other factor: