Question

How to solve the equation by completing the square. (not sure what to do with the 2x at the end of the problem)

2x(squared)+6x-14=0

Answer 1

x = 8, or -11.

Explanation:

Given:

the given expression.

`2x^2+6x-14=0`

We need to solve the given expression by completing the square.

Solution:

Rewrite the expression as:

`2x^2+6x-14=0`

Whole expression divided by 2.

`x^2+3x-7=0`

Where:

`b=3\ and\ c=-7`

Solve the given expression by the following formula.

`x^2+bx+c=(x+(b)/(2))^2-((b)/(2))^2+c=0` --------------(1)

Substitute b and c value in equation 1.

`(x+(3)/(2))^2-((3)/(2))+(-7)=0`

`(x+(3)/(2))^2-(3)/(2)-7=0`

`(x+(3)/(2))^2+(-3-7* 2)/(2)=0`

`(x+(3)/(2))^2+(-3-14)/(2)=0`

`(x+(3)/(2))^2+(-19)/(2)=0`

`(x+(3)/(2))^2-(19)/(2)=0`

Add
`(19)/(2)` both side of the equation.

`(x+(3)/(2))^2-(19)/(2)+(19)/(2)=(19)/(2)`

`(x+(3)/(2))^2=(19)/(2)`

Square root of the whole equation.

`\sqrt{(x+(3)/(2))^2}=\sqrt{(19)/(2)}`

`x+(3)/(2)=\pm(19)/(2)` --------(1)

For positive sign.

Add
`(3)/(2)` both side of the equation 1.

`x+(3)/(2)-(3)/(2)=(19)/(2)-(3)/(2)`

`x=(19)/(2)-(3)/(2)`

`x=(19-3)/(2)`

`x=(16)/(2)`

x = 8

Similarly for negative sign.

x = -11

Therefore, the value of x = 8, or -11.