How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions?

How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions?

Note:

There are many ways to solve a quadratic equation. One of these ways is by using the square root method. Watch this tutorial to see how the square root method is used to solve a quadratic equation and find imaginary solutions!

Keywords:

  • problem
  • square root method
  • quadratic equation
  • solve
  • solving
  • imaginary
  • solutions
  • i

Background Tutorials

  • Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

      • What's the Subtraction Property of Equality?What's the Subtraction Property of Equality?

      What's the Subtraction Property of Equality?

      Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Watch the video to see it in action!

  • Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

      • How Do You Find the Square Root of a Perfect Square?How Do You Find the Square Root of a Perfect Square?

      How Do You Find the Square Root of a Perfect Square?

      Taking the square root of a perfect square always gives you an integer. This tutorial shows you how to take the square root of 36. When you finish watching this tutorial, try taking the square root of other perfect squares like 4, 9, 25, and 144.

      • What's a Perfect Square?What's a Perfect Square?

      What's a Perfect Square?

      Anytime you square an integer, the result is a perfect square! The numbers 4, 9, 16, and 25 are just a few perfect squares, but there are infinitely more! Check out this tutorial, and then see if you can find some more perfect squares!

  • Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2= q that has the same solutions. Derive the quadratic formula from this form.

      • What is a Quadratic Equation?What is a Quadratic Equation?

      What is a Quadratic Equation?

      You can't go through algebra without seeing quadratic equations. The graphs of quadratic equations are parabolas; they tend to look like a smile or a frown. There's also a bunch of ways to solve these equations! Watch this tutorial and get introduced to quadratic equations!

Further Exploration

  • 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.