Use the quadratic formula to solve the quadratic equation 10x^2 + 5x = 5x - 8. Express its solutions in the form a ± bi.
First, let's rearrange the equation so all terms are on one side:
10x^2 + 5x - 5x + 8 = 0
Simplifying, we get:
10x^2 + 8 = 0
Now we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from our equation:
a = 10, b = 0, c = 8
x = (-0 ± sqrt(0^2 - 4 * 10 * 8)) / (2 * 10)
Further simplifying:
x = (± sqrt(-320)) / 20
Since the number under the square root is negative, we can simplify it by taking out the square root of -1, which is represented by "i".
x = (± sqrt(16 * -20) / 20
x = (± 4i sqrt(5)) / 20
Simplifying further:
x = (± 4i sqrt(5)) / (4 * 5)
x = (± i sqrt(5)) / 5
Therefore, the solutions to the quadratic equation 10x^2 + 5x = 5x - 8 are x = (± i sqrt(5)) / 5, expressed in the form a ± bi.