Solve by factoring:
One of the solutions to the quadratic equation 2x^2 - 9x – 5 is -1/2.
What is the other solution?
2x^2 - 9x – 5 = (2x + 1)(x - 5)
So, it's x = 5.
To solve the quadratic equation 2x^2 - 9x - 5 = 0 by factoring, we need to find two binomials that multiply together to give us the original equation.
First, we need to find the factors of 2 and -5, which are 1, 2, 5, and -5. Next, we need to find the pair of factors whose sum is equal to -9 (the coefficient of the x term). In this case, the pair of factors is -1 and 10, since -1 + 10 = 9.
We can now rewrite the quadratic equation using these factors:
2x^2 - 9x - 5 = (2x + 1)(x - 5)
From this factored form, we can see that one of the solutions to the equation is when (2x + 1) equals zero, which is -1/2.
So, setting (2x + 1) = 0, we can solve for x:
2x + 1 = 0
2x = -1
x = -1/2
Now we need to find the other solution. To do this, we set (x - 5) equal to zero:
x - 5 = 0
x = 5
Thus, the other solution to the quadratic equation 2x^2 - 9x - 5 = 0 is x = 5.