Use the quadratic formula to solve the quadratic equation 8x2+5=12x
. Express its solutions in the form a±bi
.(1 point)
First, we need to put the equation in standard form, which means setting it equal to zero. So we subtract 12x from both sides of the equation:
8x^2 - 12x + 5 = 0
Now we can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 8, b = -12, and c = 5. Substituting these values into the quadratic formula, we get:
x = (-(-12) ± √((-12)^2 - 4(8)(5))) / (2(8))
Simplifying further:
x = (12 ± √(144 - 160)) / 16
x = (12 ± √(-16)) / 16
Since the term inside the square root is negative, we know that the solutions will be complex numbers. Simplifying the square root of -16:
x = (12 ± √(16i^2)) / 16
x = (12 ± 4i) / 16
x = (3 ± i) / 4
So the solutions to the quadratic equation 8x^2 + 5 = 12x are:
x = (3 + i) / 4
x = (3 - i) / 4