QF - Solve Quadratics by Taking Square Roots (Lesson)

Solve Quadratics by Taking Square Roots

When a quadratic function is written in standard form ax2 + bx + c = 0 , factoring should be our first method that we try. But, when you see a quadratic function written like the two below we can solve by taking square roots!

x2 - 5 = 27

(x + 2)2 - 1 = 7

We do this by isolating the quantity being squared. Let's try these two problems.

Example 1

x2 - 5 = 27

x2 = 32

x = LaTeX: \pm\sqrt[2]{32}±2√32 

x = LaTeX: \pm\sqrt[2]{16}\sqrt[2]{2}±2√162√2 

x = LaTeX: \pm4\sqrt[2]{2}±42√2 

Example 2

(x + 2)2 - 1 = 7

(x + 2)2 = 8

x + 2 = LaTeX: \pm± LaTeX: \sqrt[2]{8}2√8

x + 2 = LaTeX: \pm2\sqrt[2]{2}±22√2 

LaTeX: x=-2\pm2\sqrt[2]{2}x=−2±22√2

In the examples above, our answers are written in exact form. At times, you will be asked to determine the approximate value of x. So using the example from above you would put it in decimal form.

LaTeX: x=-2\pm2\sqrt[2]{2}x=−2±22√2  which is x = 0.8 or x is approximately -4.8.

Let's try a few more problems together! 

   

Ok now let's see if you've got it, give your answers in exact form.

Solve Quadratics by Taking Square Roots Practice

  1.  -3x2 + 24 = 0
  2. (x - 3)2 - 49 = 0
  3. 2(x + 1)2 = 64
  4. 3x2 - 81 = 0

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