Question

Solve by completing the square. 4x^2 + 8x– 3=0

Answer 1

x = -1 +
`\sqrt{(7)/(4) }`, x = -1 -
`\sqrt{(7)/(4) }`

Explanation:

4
`x^(2)` + 8x - 3 = 0

First, add 3 to both sides:

4
`x^(2)` + 8x = 3

Next, divide both sides by 4:

`x^(2)` + 2x =
`(3)/(4)`

Now, add the correct number by dividing 2 by 2 and squaring it and add it to both sides:

`x^(2)` + 2x + 1 =
`(7)/(4)`

Then, factor the left side:

`(x + 1)^(2)` =
`(7)/(4)`

Next, take the square root of both sides:

x + 1 = ±
`\sqrt{(7)/(4) }`

Solve for x:

x = -1 +
`\sqrt{(7)/(4) }`, x = -1 -
`\sqrt{(7)/(4) }`