Solving Equations with Perfect Squares, Cubes, and Roots

What are the steps to solving this by completing the square?

• Subtract 21 from both sides of the equation

• Add 25 to both sides of the equation

• Rewrite the left hand side as a (binomial)²

• Take the square root of both sides of the equation

• Subtract 5 from both sides of the equation

Answer explanation

Steps for completing the square when a=1

1st: Rewrite as x² + bx = c

2nd: Take half of b, square it, then add this to both sides.

3rd: Factor the perfect square trinomial.

4th: Take the square root of both sides and solve for both cases.

5th: Write the answer using curly braces in set notation

If you have a ​ (a)   , you can solve the quadratic equation by square roots!

Remember a ​ (b)   number always has ​ (c)   real square roots, so you must solve for both cases.

• difference of squares

• perfect square trinomial

• positive

• negative

• sum of cubes

• difference of cubes

• rational

• two

• one

• three

Reorder the following steps to solve a quadratic equation when the leading coefficient is 1 (a = 1) to solve the equation by completing the square.

• Rewrite as

  x² + bx = c

• Take half of b, square it, then

  add this to both sides.

• Factor the perfect square trinomial.

• Take the square root of both sides and solve for both cases.

• Write the answer using curly braces in set notation

x² - 64 = 0

• 64

• 8

• 8 or -8

• 1 or -64

• x = 12
• x = 24
• x = 144
• x = 121

Determine the value of x in the equation below.

• 10

• -10

• ±10

• none of the above

Determine the value of x in the equation below.

• √15

• -√15

• ±√15

• none of the above

Solve for x; identify extraneous solutions (if any).

• x = 17

• x = 5

• x = 3

• no solution; x = 5 is extraneous

Solve using square roots.

• ±√9

• ±3

• ±1

• No real solution

x² = 169

• 14

• 12

• 13

• 15