# How do you solve # 2x^2 - 12x + 7 = 5#?

##### 2 Answers

Mar 28, 2018

#### Explanation:

Given:

#2x^2-12x+7=5#

Subtract

#2x^2-12x+2=0#

Divide both sides by

#0 = x^2-6x+1#

#color(white)(0) = x^2-6x+9-8#

#color(white)(0) = (x-3)^2-(2sqrt(2))^2#

#color(white)(0) = ((x-3)-2sqrt(2))((x-3)+2sqrt(2))#

#color(white)(0) = (x-3-2sqrt(2))(x-3+2sqrt(2))#

Hence:

#x = 3+-2sqrt(2)#

Mar 29, 2018

#### Explanation:

2x^2 - 12x + 2 = 0

x^2 - 6x + 1 = 0

Use the improved quadratic formula (Socratic search):

There are 2 real roots: