Final answer:
To solve the equation (5x+2)(x+1)=1, expand the equation, subtract 1, solve the quadratic equation using the quadratic formula, and simplify to find the solutions.
Step-by-step explanation:
To solve the equation (5x+2)(x+1)=1, we can expand the equation and then solve for x.
Expanding the equation gives us:
5x^2 + 7x + 2 = 1
Subtracting 1 from both sides of the equation:
5x^2 + 7x + 1 = 0
Now we can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c:
x = (-7 ± √(7^2 - 4*5*1)) / (2*5)
Simplifying further:
x = (-7 ± √(49 - 20)) / 10
x = (-7 ± √29) / 10
Therefore, the solutions to the equation (5x+2)(x+1)=1 are x = (-7 + √29) / 10 and x = (-7 - √29) / 10.