Answer:
To solve the quadratic equation 2x^2 + x - 3 = 0 by factoring, we follow these steps:
Step 1: Write the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, the equation is already in standard form: 2x^2 + x - 3 = 0.
Step 2: Factor the quadratic expression on the left-hand side of the equation. We look for two numbers that multiply to give us the constant term (c) and add to give us the coefficient of the linear term (b). In this case, c = -3 and b = 1.
The two numbers that satisfy these conditions are -3 and 1, as -3 * 1 = -3 and -3 + 1 = -2.
Step 3: Use the factored form to set each factor equal to zero and solve for x.
2x^2 + x - 3 = 0
(2x - 3)(x + 1) = 0 (factored form)
Setting each factor equal to zero:
2x - 3 = 0
2x = 3
x = 3/2
x + 1 = 0
x = -1
So the solutions to the equation are x = 3/2 and x = -1.