Solve the quadratic equation 2x2+4x=−12 . Which of the following expresses its solutions in the form a±bi ?(1 point)
Responses
−1±i5–√
negative 1 plus or minus i Start Root 5 End Root
−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–√
To solve the quadratic equation 2x^2 + 4x = -12, we need to rearrange the equation to the form ax^2 + bx + c = 0. In this case, a = 2, b = 4, and c = -12.
To find the solutions, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
x = (-4 ± √(4^2 - 4(2)(-12))) / (2(2))
x = (-4 ± √(16 + 96)) / 4
x = (-4 ± √112) / 4
x = (-4 ± √16 * √7) / 4
x = (-4 ± 4√7) / 4
x = -1 ± √7
So the solution to the quadratic equation is -1 ± √7.
So the correct answer is: −1± i√7.