Question

What are the solutions of this quadratic equation?X2 - 10x= -34A.r=-8, -2B.r= 5 + 3iC.r=-5 + 3iD.r=-5 + 159

Answer 1

The given equation is-

$x^2-10x=-34$

First, we move the independent term to the other side.

$x^2-10x+34=0$

Now, we have to use the quadratic equation to find the solutions.-

$x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Where, a = 1, b = -10, and c = 34.

Replacing these values in the formula, we have.

$\begin{gathered} x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(1)(34)}}{2(1)} \\ x_{1,2}=\frac{10\pm\sqrt[]{100-136}}{2}=\frac{10\pm\sqrt[]{-36}}{2} \end{gathered}$

But, there's no square root of -36 because it's a negative. To solve this issue, we use complex numbers that way, we would have solutions.

$x_{1,2}=\frac{10\pm\sqrt[]{36}i}{2}=\frac{10\pm6i}{2}=5\pm3i$

Therefore, the solutions are

$\begin{gathered} x_1=5+3i \\ x_2=5-3i \end{gathered}$The right answer is B.