Use the quadratic formula to solve the quadratic equation 10x^2 + 5x = 5x - 8. Express its solutions in the form, a ± bi
To solve the quadratic equation 10x^2 + 5x = 5x - 8, we need to rewrite it in the form ax^2 + bx + c = 0. In this case, the equation simplifies to 10x^2 + 5x - 5x + 8 = 0, which further simplifies to 10x^2 + 8 = 0.
Comparing this equation to the standard form ax^2 + bx + c = 0, we have a = 10, b = 0, and c = 8. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (0 ± √(0^2 - 4(10)(8))) / (2(10))
x = (± √(-320)) / 20
Since the expression √(-320) represents the square root of a negative number, we can simplify it as:
√(-320) = √(320) * √(-1) = √(16 * 20) * i = 4√5i
Therefore, the solutions to the quadratic equation are:
x = (± 4√5i) / 20
x = ± (2/5)√5i
Expressing it in the form a ± bi, we have:
x = (2/5)(√5)i, -(2/5)(√5)i