Question

Solve for x.

2x2+4x−1=0

Enter the answer in the box below:

X = or X=

Answer 1

Answer:x=−1+126or x=−1+−126

Explanation:

In the image

Answer 2

`x=(-2 +√(6))/(2), \quad x=(-2 -√(6))/(2)`

Explanation:

Given quadratic equation:

`2x^2+4x-1=0`

Solve by completing the square

Move the constant to the right side of the equation:

`\implies 2x^2+4x-1+1=0+1`

`\implies 2x^2+4x=1`

Factor out the common factor of 2 from the left side:

`\implies 2(x^2+2x)=1`

`\implies x^2+2x=(1)/(2)`

Add the square of half the coefficient of the term in x to both sides of the equation:

`\implies x^2+2x+\left((2)/(2)\right)^2=(1)/(2)+\left((2)/(2)\right)^2`

`\implies x^2+2x+(1)^2=(1)/(2)+(1)^2`

`\implies x^2+2x+1=(1)/(2)+1`

`\implies x^2+2x+1=(3)/(2)`

Factor the perfect square trinomial on the left side of the equation:

`\implies (x+1)^2=(3)/(2)`

Square root both sides:

`\implies √((x+1)^2)=\sqrt{(3)/(2)}`

`\implies x+1=\pm(√(3))/(√(2))`

`\implies x+1=\pm(√(3))/(√(2)) \cdot (√(2))/(√(2))`

`\implies x+1=\pm(√(6))/(2)`

Subtract one from both sides:

`\implies x+1-1=\pm(√(6))/(2)-1`

`\implies x=-1\pm(√(6))/(2)`

`\implies x=-(2)/(2)\pm(√(6))/(2)`

`\implies x=(-2 \pm √(6))/(2)`