Solve for x 6x^2+12x+7=0

Problem

6*x2+12*x+7=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=6 b=12 and c=7

2. Apply the quadratic formula which is given by x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the formula:

x=(−12±√(,12−4*(6)*(7)))/(2*(6))

4. Simplify the expression inside the square root (the discriminant):

x=(−12±√(,144−168))/12

x=(−12±√(,−24))/12

5. Simplify the radical using the imaginary unit i where √(,−24)=√(,−1⋅4⋅6)=2*i√(,6)

x=(−12±2*i√(,6))/12

6. Divide each term in the numerator by the denominator to find the final values of x

x=(−12)/12±(2*i√(,6))/12

x=−1±(i√(,6))/6

Final Answer

x=−1±(i√(,6))/6

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