Question

How do you solve by completing the square for `2x^2+10x-4=0`?

Answer 1

`2(x + 5/2)^2 - 33/2`

Explanation:

Take 2 out of the equation:
`2(x^2 + 5x - 2) = 0`

Complete the square in the brackets:
`2((x + 5/2)^2 - 25/4 - 2)`

Simplify the equation:
`2((x + 5/2)^2 - 33/4)`
`2(x + 5/2)^2 - 33/2`

Answer 2

`2x^2 +10x -4=0`

First divide by `2` so that we have `1x^2" "a=1`

`x^2 +5x -2=0`

`x^2 +5x " "=2" "larr` move the constant to the RHS

`x^2+5x+ (5/2)^2 = 2+(5/2)^2" "larr` add `(b/2)^2` to both sides.

By this process you have written the left side as a 'perfect square'
This step is the 'completing the square '- add in the missing term to create a square.

Write the left side as the square of a binomial.

`(x+5/2)^2 = 4 1/2`

`x +5/2 = +-sqrt(9/2)" "larr` find the square root of both sides.

Find the two possible solutions:

`x = 3/(+sqrt2) -2.5 = -0.379` (3 dp)

`x = 3/(-sqrt2)-2.5 = -4.624`