How do you solve #x^2+4x=285#?
2 Answers
15, - 19
Explanation:
Solving by the new Transforming Method (Google, Socratic Search).
Find 2 real roots, with opposite signs (ac < 0), knowing sum (-b = -4) and product (-285).
Compose factor pairs of (-285) --> (5, - 57)(15, - 19). This last sum is
(15 - 19 = - 4 = - b).
The 2 real roots are: 15 and - 19.
Using AC Method.
Find 2 numbers, knowing sum (b = 4) and product (-285).
They are: (19, - 15) --> sum = 4 and product = -285
Split the term 4x into 19x and - 15 x
Factor by grouping:
x(x + 19) - 15(x + 19) = (x + 19)(x - 15) = 0
Solving binomials:
x + 19 = 0 --> x = - 19
x - 15 = 0 --> x = 15
Here's a simpler way to solve: by completing the square.
(Also the answer is
Explanation:
To solve by completing the square we first have to realize that
1.) The first step in completing the square is to move
2.) Now that we have the equation
3.) Does anything about the left side of the equation catch your eye? It should because the left side is now a perfect square trinomial, and can be factored, and when you factor it, you are left with the equation
4.) Take the square root of both sides of the equation to isolate
5.) Because there is a
6.) By solving for
Hope this helps!