x^2+√2x+1/2=0

Solve using the quadratic formula and use complex numbers.

x = (-√2 ± √(2 - 4(1)(1/2)) )/2

= - √2/2

ahh, then it must have factored
sure enough

(x + √2/2)^2 = 0
x = -√2/2

no need for complex numbers, the root is real.

Thank u very much, I was also confused cause I didn't understand why we needed complex numbers :)

√2xsquare-3/√2x+1/√2=0

A=√2
B=-3/√2
C=1/√2
-b+-√bsquare -4ac/2a
(-3/√2)+-√(-3/√2) square-4.√2.1/√2 /2√2

To solve the quadratic equation x^2 + √2x + 1/2 = 0 using the quadratic formula, we first need to identify the coefficients of the quadratic equation. In this case, the coefficients are:

a = 1 (coefficient of x^2)
b = √2 (coefficient of x)
c = 1/2 (constant term)

The quadratic formula states that for the equation ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Now, let's substitute the values into the quadratic formula:

x = (-(√2) ± √((√2)^2 - 4(1)(1/2))) / (2(1))

Simplifying this equation further:

x = (-√2 ± √(2 - 2)) / 2

Notice that the term inside the square root, (2 - 2), evaluates to zero. Therefore, the result is:

x = (-√2 ± √0) / 2

Since square root of zero is zero, we have:

x = (-√2 ± 0) / 2

Simplifying further, we obtain:

x = -√2 / 2 or x = √2 / 2

These are the two solutions to the given quadratic equation.