Question

6x²+6x-2=0 using completing square method​

Answer 1

Answer: x = ±
`( √(21)-3 )/(6)`

Explanation:

Given equation. We are being asked to solve for x by completing the square.

6x² + 6x - 2 = 0

First, we will isolate the constant.

6x² + 6x = 2

Next, we will factor out a 6.

6(x² + x) = 2

Now, we will add and subtract (b/2)^2. Remember that this is being multiplied by 6 when we remove it from the parentheses.

6(x² + x +
`(1)/(4)`) -
`(3)/(2)` = 2

Then, we will add
`(3)/(2)` to both sides of the equation.

6(x² + x +
`(1)/(4)`) =
`(7)/(2)`

Now, we can divide both sides of the equation by 6.

x² + x +
`(1)/(4)` =
`(7)/(12)`

Next, factor.

(x +
`(1)/(2)`)² =
`(7)/(12)`

Then, solve for x by taking the square root of both sides of the equation and isolating the x-variable.

x = ±
`( √(21)-3 )/(6)`