Solve the equation to find the value of x 3x (12x + 1) and (16x - 7)
To solve the equation 3x(12x + 1) = (16x - 7), we can distribute the 3x on the left side of the equation:
36x^2 + 3x = 16x - 7
Moving all terms to one side of the equation, we get:
36x^2 + 3x - 16x + 7 = 0
Simplifying, we have:
36x^2 - 13x + 7 = 0
We can now solve this quadratic equation using factoring, completing the square, or the quadratic formula. However, this quadratic equation does not easily factor, and completing the square or the quadratic formula would be quite tedious. Therefore, we can use the quadratic formula to find the values of x:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 36, b = -13, and c = 7. Plugging in these values:
x = (-(-13) ± √((-13)^2 - 4(36)(7))) / (2(36))
x = (13 ± √(169 - 1008)) / 72
x = (13 ± √(-839)) / 72
Since the discriminant (√(-839)) is negative, the equation has no real solutions.