Solve the quadratic equation: \$ 4x^2 + 4\sqrt2 x + 2 = 0 \$

To solve the quadratic equation \$4x^2 + 4\sqrt2 x + 2 = 0\$, we can use the quadratic formula. The quadratic formula states that for an equation in the form \$ax^2 + bx + c = 0\$, the solutions for x can be found using the formula

\$x = (-b ± \sqrt (b^2 - 4ac)) / (2a)\$

For the equation \$ 4x^2 + 4\sqrt2 x + 2 = 0\$ then, substituting these values into the quadratic formula, we get

a = 4, b = \$4 \sqrt2\$, and c = 2

\$x = (- 4 \sqrt2 ± \sqrt ((4 \sqrt2)^2 - 4 times 4 times 2)) / (2 times 4)\$

\$x = (- 4 \sqrt2 ± \sqrt(32 - 32)) / 8\$

This gives us possible solution

\$x = (- \cancel(4) \sqrt2 ) / \cancel8^2\$

\$x = - \sqrt2/2 or x = - 1/\sqrt2 \$

So the solution to the quadratic equation \$4x^2 + 4\sqrt2 x + 2 = 0\$ is \$x = - \sqrt2/2 \$.

Option

B

Can you summarize what you’ve understood in the above steps?