Solve the quadratic equation 2x2+4x=−12 . Which of the following expresses its solutions in the form a±bi ?(1 point) Responses −2±2i5–√ negative 2 plus or minus 2 i Start Root 5 End Root −1±i7–√ negative 1 plus or minus i Start Root 7 End Root −1±i5–√ negative 1 plus or minus i Start Root 5 End Root 1±i5–√
To solve the quadratic equation 2x^2 + 4x = -12, we first need to rearrange it to the form ax^2 + bx + c = 0.
So, we have 2x^2 + 4x + 12 = 0.
Now, we can apply the quadratic formula to find the solutions of the equation.
The quadratic formula is x = (-b ± √(b^2 - 4ac))/(2a).
In our case, a = 2, b = 4, and c = 12.
Inserting these values into the quadratic formula, we have x = (-4 ± √(4^2 - 4(2)(12)))/(2(2)).
Simplifying further, we get x = (-4 ± √(16 - 96))/(4).
Now, evaluating the square root, we have x = (-4 ± √(-80))/(4).
We can simplify the square root as follows: √(-80) = √(-1) * √(80) = i√(80).
So, we have x = (-4 ± i√(80))/(4).
Simplifying further, we get x = (-4 ± 4i√(5))/(4).
Now, we can cancel out the common factor of 4 in the numerator and denominator:
x = (-1 ± i√(5)).
Therefore, the solutions of the quadratic equation 2x^2 + 4x = -12 in the form a ± bi are -1 ± i√(5).
The correct answer from the given options is −1±i5–√.