A quadratic equation is a mathematical expression that is usually written in the form of ax2 + bx + c = 0, where a, b and c are real numbers and ‘x’ is an unknown variable. Solving a quadratic equation can be both tricky and exciting. It requires the use of algebraic techniques, such as factoring and graphing. In this article, we will look at how to solve a quadratic equation step by step.
Step 1 – Factor the Quadratic Equation
The first step in solving a quadratic equation is to factor the equation. To do this, use the “FOIL” method. First, multiply the first and last terms of the equation (a and c). This will give you the “outside” terms of the equation. Next, multiply the two middle terms (b and c). This will give you the “inside” terms. Finally, add the two products together to get the equation in its factorised form.
Step 2 – Identify the Roots
Once the equation has been factorised, it’s time to identify the roots. To do this, set each factor equal to zero and solve for x. This will give you the two roots of the equation. The roots are the two values of x that make the equation true.
Step 3 – Use the Quadratic Formula
If you are unable to factor the equation, you can use the quadratic formula to solve the equation. The quadratic formula is: x = [-b ± √(b2 – 4ac)]/2a. To use the formula, plug in the values of a, b and c into the equation and solve for x. This will give you the two roots of the equation.
Step 4 – Graph the Quadratic Equation
Another way to solve a quadratic equation is to graph it. To do this, plot the points given by the equation on a graph. This will give you a parabola. From there, you can identify the roots of the equation by finding the x-intercepts of the parabola. The x-intercepts are the two points where the parabola crosses the x-axis.
Step 5 – Check Your Answer
Once you have identified the roots of the equation, it’s important to check your answer to make sure it is correct. To do this, plug the values of x back into the equation and make sure the equation is true. If it is, then your answer is correct. If it isn’t, then you may need to go back and re-examine your work.
Conclusion
Solving a quadratic equation can be tricky but it doesn’t have to be. By following the steps outlined in this article, you can easily solve a quadratic equation. Just remember to factor, identify the roots, use the quadratic formula and graph the equation, and then check your answer to make sure it is correct. Good luck!