Use the quadratic formula to solve the quadratic equation below. Express its solution in the form of

a ± bi. 8x^2 + 10x = 10x -4

1 answer

To solve the quadratic equation \( 8x^2 + 10x = 10x - 4 \), we start by rearranging the equation to standard form:

\[ 8x^2 + 10x - 10x + 4 = 0 \]

This simplifies to:

\[ 8x^2 + 4 = 0 \]

Next, we can rewrite this as:

\[ 8x^2 = -4 \]

Dividing both sides by 8 gives:

\[ x^2 = -\frac{4}{8} = -\frac{1}{2} \]

To solve for \( x \), we take the square root of both sides:

\[ x = \pm \sqrt{-\frac{1}{2}} \]

We can express this as:

\[ x = \pm \sqrt{\frac{1}{2}} \cdot \sqrt{-1} = \pm \frac{1}{\sqrt{2}} \cdot i \]

This can be simplified further by rationalizing the denominator:

\[ x = \pm \frac{\sqrt{2}}{2}i \]

Therefore, the solutions of the quadratic equation in the form of \( a \pm bi \) is:

\[ x = 0 \pm \frac{\sqrt{2}}{2}i \]

So the solutions are:

\[ x = \frac{\sqrt{2}}{2}i \quad \text{and} \quad x = -\frac{\sqrt{2}}{2}i \]