Solve Using Completing the Square

Solve: (x + 6)² = 1

• -5, -7

• 5, 7

• 5, -7

• -5, 7

Solve: 2(x - 3)² - 14 = 18

• 1, 7

• -1, 7

• -1, -7

• 1, -7

Solve by completing the square:

k² − 12k + 20 = 0

• k = 10 and 2

• k = -6 and -6

• k = 22 and -10

• k = -2 and 6

Solve by completing the square.
x² +12x = 5

• X = 6 + √41 or  6 − √41

• X= 35 or 47

• X = −6 + √41 or  −6 − √41

• X = √35 or √47

Complete the Square and solve the equation.
m² - 16m = -59

• 8

• 8 ± √ 5

•  ± √ 13

• -8 ± √ 5

Kevin wants to solve the equation by completing the square. What values complete the equation?

• 8

• 64

• 16

• 4

• 256

x² + 10x = -9

Steps to solve by completing the square are:

​ (a)  

​ (b)  

​ (c)  

​ (d)  

​ ​ (e)  

• Take half of 10 and square it.

• Add 25 to both sides.

• Solve the perfect square trinomial

• Take the square root of both sides

• Solve for x to get a solution.

• Take half of -9 and add to both sides.

• Divide all terms by 10

• Set equal to zero.

Kevin wants to solve the equation by completing the square. What values complete the equation?

• 8

• 64

• 16

• 4

• 256

x² + 10x = -9 Steps to solve by completing the square are:

• Take half of 10 and square it.

• Add 25 to both sides.

• Solve the perfect square trinomial

• Take the square root of both sides

• Solve for x to get a solution.

• Take half of -9 and add to both sides.

• Divide all terms by 10

• Set equal to zero.

Solve for the POSITIVE SOLUTION ONLY of x by completing the square. ROUND to the nearest hundredth (2 decimal places).

Mathematical Equivalence

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