Question

solve the equation. 2x² + 6 = -34 the solutions are x = and x =

Explanation:

Step1: Isolate the quadratic term

Subtract 6 from both sides of the equation $2x^{2}+6=-34$. We get $2x^{2}=-34 - 6=-40$.

Step2: Solve for $x^{2}$

Divide both sides of the equation $2x^{2}=-40$ by 2. So $x^{2}=\frac{-40}{2}=-20$.

Step3: Find the value of $x$

Take the square - root of both sides. Since we have a negative number on the right - hand side, the solutions are complex numbers. $x=\pm\sqrt{-20}=\pm2\sqrt{5}i$.

Answer:

$x = 2\sqrt{5}i$ and $x=-2\sqrt{5}i$