quadratic equations
Solve: 2x^2-5x=3
2x^2 -5x -3 = 0
(2x + 1)(x -3) = 0
x = -1/2 or 3
To solve the quadratic equation 2x^2 - 5x = 3, you need to follow these steps:
Step 1: Rewrite the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, you already have it in that form: 2x^2 - 5x - 3 = 0.
Step 2: Factor the quadratic expression on the left side of the equation. To do this, find two numbers that multiply to give -6 and add up to give -5. The numbers -6 and 1 fit this criteria, so you can factor the expression as (2x + 1)(x - 3) = 0.
Step 3: Set each factor equal to 0 and solve for x. You will have two separate equations to solve:
2x + 1 = 0 or x - 3 = 0
Solving the first equation, you get:
2x = -1
x = -1/2
Solving the second equation, you get:
x = 3
So the solutions to the quadratic equation 2x^2 - 5x = 3 are x = -1/2 and x = 3.