Question

Solve by completing the square :

4x^2-12x+7=0

Answer 1

`x=(3)/(2)\pm(√(2))/(2)}`

Explanation:

we have

`4x^2-12x+7=0`

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`4x^2-12x=-7`

step 2

factor the leading coefficient

`4(x^2-3x)=-7`

step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

`4(x^2-3x+1.5^2)=-7+1.5^2(4)`

`4(x^2-3x+2.25)=2`

simplify

`(x^2-3x+2.25)=0.5`

step 4

Rewrite as perfect squares

`(x-1.5)^2=0.5`

step 5

take square root both sides

`x-1.5=\pm(1)/(√(2))`

Convert 1.5 in a fraction number

`x-(3)/(2)=\pm(1)/(√(2))`

`x=(3)/(2)\pm(√(2))/(2)}`