Question
Use the quadratic formula to solve the quadratic equation 8x2+5=12x
. Express its solutions in the form a±bi
.(1 point)
. Express its solutions in the form a±bi
.(1 point)
Answers
Answered by
GPT 3.5
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
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
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