Solutions to Equations with Squares and Cubes

A perfect _________________ is the result after multiplying a number by itself three times.

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

• Take the square root of both sides of the equation

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

• Subtract 5 from both sides of the equation

• Subtract 21 from both sides of the equation

• Add 25 to 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

Solve by the Square Root method: x² = 16

• ± 4

• ± 8

• 4i

• 8i

• -4i

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

When is a quadratic equation factorable?

• When the diagonal

  (ax=y) is a perfect square

• When the difference

  (d=ax²−c) is a perfect square

• When the difference

  (d=ax²−c) is a perfect cube

• When the discriminant

  (d=b²−4ac) is a perfect cube

• When the discriminant

  (d=b²−4ac) is a perfect square

What is another word for roots of an equations?

(Select all choices that apply.)

• y-intercepts

• zeros

• vertex

• x-intercepts

• solutions

Order the following steps for solving quadratic equations by factoring.

• Set each factor equal to zero, and solve each for the variable.

• Write the answer using curly braces in set notation.

• Set the quadratic equation equal to zero.

• Factor the left side.

• bx

• square roots

• cx

• discriminant

• quadratic formula

• Isolate the

• Take the square root of both sides.

• Eliminate the

Reorder the following steps to solve a quadratic equation by using the quadratic formula.

• Simplify using the order of operations

  (PEMDAS)

• Make sure the equation is

  set equal to 0 and written

  in standard form.

  ax² + bx + c = 0

• Identify a, b, and c.

• Substitute these values

  into the formula

• Write the answer using curly braces in set notation

What number, n, cubed is equal to -216?

n³ = -216

• -6

• 6

• -7

• 72