Solving a Quadratic with Square Roots

Solve the equation by completing the square and then finding the roots. 
x²+ 6x - 4 = 36

• x = -7, 7

• x = 4, -10

• x = -4 +- √7

• x = 10, -4

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

x² = 100

• 10

• 10 or -10

• 50

• 50 or -50

x²=25

• x = 5

• x = -5

• x = ±25

• x = ±5

2x²=98

• 49, -49

• 9.89, -9.89

• 7, -7

• no solution 

Solve using square roots.

k² - 6 = 43

• k = √37

• k = 37 or - 37

• k = 7, k = -7

• no real solution

Solve by taking square roots:

5m² + 1 = 6

• m = 1

• m = 1 or -1

• m = √7

• m = 7/5 m = -7/5

2d² = 8

• 4

• -2

• -4, 4

• -2, 2

• 5, -5

• 2.23, -2.23

• 2.3

• 5

Solve by taking the square root:

4x² = 100

• x = ±10

• x = ±25

• x = ±5

• x = 5