Question

Solve −2x2 +3x − 9 = 0.

x equals quantity of 3 plus or minus 3i square root of 7 all over 4
x equals quantity of 3 plus or minus 9i square root of 7 all over 4
x equals quantity of negative 3 plus or minus 3i square root of 7 all over 4
x equals quantity of negative 3 plus or minus 9i square root of 7 all over 4

Answer 1

Answer: A

Step-by-step explanation: x equals quantity of 3 plus or minus 3i square root of 7 all over 4

Answer 2

To solve the equation -2x^2 + 3x - 9 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = -2, b = 3, and c = -9. Substituting these values into the quadratic formula, we get:

x = (-3 ± √(3^2 - 4(-2)(-9))) / (2(-2))

Simplifying this expression further, we have:

x = (-3 ± √(9 - 72)) / (-4)

x = (-3 ± √(-63)) / (-4)

Now, we can simplify the square root of -63. Since the square root of a negative number is not a real number, we can express it as a complex number by introducing the imaginary unit i.

The square root of -63 can be written as √(63) * i, where i represents the imaginary unit.

So, our expression becomes:

x = (-3 ± √(63) * i) / (-4)

Now, we can simplify the expression inside the square root:

x = (-3 ± 3√(7) * i) / (-4)

Finally, we can simplify the expression further by factoring out a common factor of 3 from the numerator:

x = (3(-1 ± √(7) * i)) / (-4)

Simplifying the expression, we get:

x = (3 ± 3√(7) * i) / 4

Therefore, the correct solution to the equation -2x^2 + 3x - 9 = 0 is:

x = (3 ± 3√(7) * i) / 4