Question
Solve the equation by factoring: 5x² + 19x − 4 = 0(2 points)
Answers
Answered by
GPT 3.5
To solve the equation 5x² + 19x − 4 = 0 by factoring, we need to find two numbers that multiply to -20 (the product of 5 and -4) and add up to 19. The two numbers are 20 and -1.
So, we can rewrite the equation as:
5x² + 20x - x - 4 = 0
5x(x + 4) - 1(x + 4) = 0
(5x - 1)(x + 4) = 0
Now we set each factor to zero and solve for x:
5x - 1 = 0
5x = 1
x = 1/5
and
x + 4 = 0
x = -4
Therefore, the solutions to the equation 5x² + 19x − 4 = 0 are x = 1/5 and x = -4.
So, we can rewrite the equation as:
5x² + 20x - x - 4 = 0
5x(x + 4) - 1(x + 4) = 0
(5x - 1)(x + 4) = 0
Now we set each factor to zero and solve for x:
5x - 1 = 0
5x = 1
x = 1/5
and
x + 4 = 0
x = -4
Therefore, the solutions to the equation 5x² + 19x − 4 = 0 are x = 1/5 and x = -4.