Final answer:
The real solutions to the equation are x = 0 and x = -1/7.
Step-by-step explanation:
This quadratic equation can be solved using the quadratic formula. The given equation is:
(-7x-3)² + 4(-7x-3) + 3 = 0
By expanding and simplifying the equation, we get:
49x² + 42x + 9 + (-28x - 12) + 3 = 0
Combine like terms and rearrange the equation:
49x² + 14x = 0
Apply the quadratic formula:
x = (-b ± √(b² - 4ac))/(2a)
From the equation, the coefficients are:
a = 49, b = 14, c = 0
Substitute these values into the formula:
x = (-14 ± √(14² - 4*49*0))/(2*49)
Simplify further:
x = (-14 ± √(196))/(98)
x = (-14 ± 14)/(98)
x = 0 or x = -1/7
Therefore, the real solutions to the equation are x = 0 and x = -1/7.