How do I solve by factoring
(x2/5) – 3 – 3x = – 3
To solve the equation (x^2/5) - 3 - 3x = -3 by factoring, first rearrange the equation to set it equal to zero:
(x^2/5) - 3 - 3x + 3 = -3 + 3
(x^2/5) - 3x = 0
To factor this quadratic equation, you need to find two numbers that multiply to give the constant term (-3/5) and add up to give the coefficient of the x-term (-3).
The constant term is -3/5, which can be factored as (-1/5) * (3/1) or (1/5) * (-3/1). However, neither combination adds up to -3.
Since the quadratic equation cannot be factored easily with whole numbers, you can use the quadratic formula to find the roots.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1/5, b = -3, and c = 0.
Substituting the values into the quadratic formula:
x = (3 ± √((-3)^2 - 4*(1/5)*(0))) / (2*(1/5))
Simplifying further:
x = (3 ± √(9 - 0)) / (2/5)
x = (3 ± √(9)) / (2/5)
x = (3 ± 3) / (2/5)
Now, consider the two cases separately:
1. When x = (3 + 3) / (2/5):
x = (6) / (2/5)
x = (6) * (5/2)
x = 15
2. When x = (3 - 3) / (2/5):
x = (0) / (2/5)
x = 0
Therefore, the solutions to the equation (x^2/5) - 3 - 3x = -3 are x = 15 and x = 0.