Solving Quadratic Equations

Quadratic equations are equations where the highest power is 2. Quadratic equations look like this: ax ² + bx + c. Sometimes the b value is missing, other times the c value is missing. Quadratic equations can be solved two different ways by factoring or using the quadratic formula. Solving a quadratic equation means finding the  roots of the equation. Roots are the solutions which may satisfy the equation. 

Factoring:
Factoring a quadratic equation is only possible if the equation is factor-able. For example: 

Here the equation is x ² + x - 42. It can be factored to (x+7)(x-6). Than you set them to zero and solve for x. The solutions for x are -7 and 6. 

The Quadratic Formula:
The quadratic formula works for every quadratic equation even the ones that can be factored. The quadratic formula is  . In order to solve the equation using the formula you must substitute the numbers in the equation. For example:

Here the equation is x ² + 2x - 3. The a is 1, b is 2 and c is -3. Here all the numbers are plugged in and solved for. Reminder, always find both solutions of the equation by subtracting and adding the numbers properly using the order of operations. The roots for this solution is 1 and -3.

Question:
What are the roots for this quadratic equation? x² + x – 4 = 0





Sources:

• http://www.google.com/url?source=imglanding&ct=img&q=http://www.gradeamathhelp.com/image-files/solve-by-factoring.jpg&sa=X&ei=pWuMUOOSNcr20gHqpID4Dw&ved=0CAkQ8wc&usg=AFQjCNE7eD9GbzXwexGHnCXHnZOttkkdnw
• http://www.google.com/url?source=imglanding&ct=img&q=http://www.mathwarehouse.com/quadratic/images/formula_solution_-3_and_1.gif&sa=X&ei=Bm-MUPCmD4f50gHJtoHgCg&ved=0CAkQ8wc&usg=AFQjCNHsIqk4Z6puR4MNs44agEguLJJh_A