Solve by factoring:
2a^2-3a= -5
2a^2 - 3a + 5 = 0
(2a - 5)(a + 1) = 0
a = 5/2 or a = -1
6x^2+19x=10
To solve the quadratic equation 2a^2 - 3a = -5 by factoring, we need to rearrange the equation into the form ax^2 + bx + c = 0, where a, b, and c are coefficients. In this case, we have:
2a^2 - 3a + 5 = 0
Now, let's factor this equation. Since the coefficient of a^2 is 2, we can look for two binomials in the form (ax + b)(cx + d) that multiply to give 2a^2. The coefficients a, b, c, and d should satisfy the equation ac = 2, bd = 5, and ad + bc = -3.
We can see that 2 and 1 are the only factors of 2a^2. Therefore, we try factoring it as:
(2a - 1)(a + 5) = 0
Now, by the zero-product property, we set each factor equal to zero and solve for a:
2a - 1 = 0 or a + 5 = 0
Solving the first equation:
2a - 1 = 0
2a = 1
a = 1/2
Solving the second equation:
a + 5 = 0
a = -5
Therefore, the solutions to the quadratic equation 2a^2 - 3a = -5 are a = 1/2 and a = -5.