What are the steps involved in solving a quadratic equation?
To solve a quadratic equation, follow these steps:
Step 1: Write down the quadratic equation in the standard form, which is ax^2 + bx + c = 0. Here, 'a', 'b', and 'c' are coefficients representing different terms of the equation.
Step 2: If the quadratic equation is not already in standard form, rearrange the equation to bring all terms on one side of the equation, with the constant term on the right side. For example, if you have the equation x^2 + 5x - 6 = 0, bring all terms to the left side: x^2 + 5x - 6 = 0.
Step 3: Identify the values of 'a', 'b', and 'c'. These coefficients will be used to plug into the quadratic formula.
Step 4: Apply the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a). This formula provides you with the two possible values for 'x' that will satisfy the quadratic equation.
Step 5: Evaluate the expression inside the square root, i.e., calculate the discriminant (b^2 - 4ac). The discriminant determines the number and nature of solutions.
Step 6: If the discriminant is positive, take the square root of the discriminant and plug it into the quadratic formula. This will give you two distinct real solutions for 'x'.
Step 7: If the discriminant is zero, it means there is only one real solution. Plug the value of the square root of the discriminant (which is zero in this case) into the quadratic formula.
Step 8: If the discriminant is negative, the quadratic equation has no real solutions. In this case, x will be complex numbers. The imaginary part of 'x' will involve 'i', the imaginary unit.
Step 9: Solve the equation using the quadratic formula by substituting the values of 'a', 'b', and 'c'. Calculate both solutions for 'x' if they exist.
Step 10: Simplify and approximate the solution, if necessary. Round the answers to an appropriate number of decimal places, depending on the context of the problem.
Remember, practice is essential to become proficient in solving quadratic equations.