Solve the quadratic equation 12x2−12x+4=−3x . Which of the following expresses its solutions in the form a±bi ?(1 point) Responses 38±111√24i Start Fraction 3 over 8 End Fraction plus or minus Start Fraction Start Root 111 End Root over 24 End Fraction i 38+111√24i Start Fraction 3 over 8 End Fraction plus Start Fraction Start Root 111 End Root over 24 End Fraction i 38±273√24i Start Fraction 3 over 8 End Fraction plus or minus Start Fraction Start Root 273 End Root over 24 End Fraction i −38±111√24i
To solve the quadratic equation 12x^2 - 12x + 4 = -3x, we need to set the equation equal to zero by moving all terms to one side:
12x^2 - 12x + 4 + 3x = 0
Combine like terms:
12x^2 - 9x + 4 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In our case, a = 12, b = -9, and c = 4. Plugging these values into the quadratic formula, we get:
x = (9 ± √((-9)^2 - 4*12*4))/(2*12)
= (9 ± √(81 - 192))/(24)
= (9 ± √(-111))/(24)
Therefore, the expression that expresses the solutions in the form a ± bi is:
38 ± 111√(-1)/24
Simplifying further, we can write it as:
38 ± 111i√(1)/24
38 ± 111i/24
So the correct answer is 38 ± 111i/24.