select the correct answer.\nwhat are the solutions of this quadratic equation?\n$x^{2}-10x = - 34$\na…

Explanation:

Step1: Rewrite in standard form

Rewrite $x^{2}-10x = - 34$ as $x^{2}-10x + 34=0$.

Step2: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 1$, $b=-10$, $c = 34$.

Step3: Use quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: [ \begin{align*} x&=\frac{-(-10)\pm\sqrt{(-10)^{2}-4\times1\times34}}{2\times1}\ &=\frac{10\pm\sqrt{100 - 136}}{2}\ &=\frac{10\pm\sqrt{- 36}}{2}\ &=\frac{10\pm6i}{2}\ &=5\pm3i \end{align*} ]

Answer:

B. $x = 5\pm3i$