How do you solve 2x ^ { 2} + 57x = 4972x2+57x=497?
2 Answers
Explanation:
First we must convert our initial equation so that it fits satisfies
2x^2 + 57x = 497 2x2+57x=497 becomes2x^2 + 57x - 497 = 0 2x2+57x−497=0 .
From here we conclude the following:
a=2a=2
b=57b=57
c=-497c=−497
Now we use the quadratic formula to find the value of
x = (-b +- sqrt(b^2 -4ac))/(2a)x=−b±√b2−4ac2a
x = (-57 +- sqrt(57^2 -4(2)(-497)))/(2(2))x=−57±√572−4(2)(−497)2(2)
x = (-57 +- sqrt(3249 -8(-497)))/(4)x=−57±√3249−8(−497)4
x = (-57 +- sqrt(3249 + 3976))/(4)x=−57±√3249+39764
x = (-57 +- sqrt(7225))/(4)x=−57±√72254
x = (-57 +- 85)/(4)x=−57±854
x = (-57 + 85)/4 x=−57+854 ,x=(-57-85)/4x=−57−854
x = (28)/(4) x=284 ,x = (-142)/(4) x=−1424
x = 7x=7 ,x=-35.5x=−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: