How Do You Solve a Quadratic Equation by Completing the Square?

Note:

One of the many ways you can solve a quadratic equation is by completing the square. In this method, you want to turn one side of the equation into a perfect square trinomial. This tutorial takes you through the steps of solving a quadratic equation by completing the square. Check it out!

Keywords:

problem
skill
quadratic equation
completing the square
complete the square
perfect square
square root

Background Tutorials

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- How Do You Evaluate an Algebraic Expression?
  
  Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.
Factor a quadratic expression to reveal the zeros of the function it defines.
- How Do You Use a Shortcut to Factor a Perfect Square Trinomial?
  
  Factoring a perfect square trinomial? Did you know there's a shortcut to factoring this special kind of trinomial? Check it out! It's pretty cool, and it may make this process a little faster!
- How Do You Factor a Polynomial by Guessing and Checking?
  
  Factoring trinomials can by tricky, but this tutorial can help! Follow along as a trinomial is factored using the guess and check method. What, no possibilities work? The trinomial must be prime! Watch this tutorial and see what happens!
Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- How Do You Find the a, b, and c Values of a Quadratic Function?
  
  When you're dealing with quadratic equations, it can be really helpful to identify a, b, and c. These values are used to find the axis of symmetry, the discriminant, and even the roots using the quadratic formula. It's no question that it's important to know how to identify these values in a quadratic equation. This tutorial shows you how!