Question

Solve (2c-1) (3c+1)=11 Give each of your answers as a integer or a fraction in its simplest form.

Answer 1

To solve the equation (2c-1)(3c+1)=11, we need to multiply the terms inside the parentheses, combine like terms, and solve a quadratic equation using the quadratic formula. The solutions to the equation are c=(-1±√73)/6.

Step-by-step explanation:

To solve the equation (2c-1)(3c+1)=11, we need to multiply the terms inside the parentheses first:

6c^2-c+3c-1=11

Combine like terms:

6c^2+2c-1=11

Move 11 to the left side:

6c^2+2c-12=0

Now, we have a quadratic equation in the form ax^2+bx+c=0. We can solve this equation using the quadratic formula:

c=(-b±√(b^2-4ac))/(2a)

For this equation, a=6, b=2, and c=-12. Plugging in these values into the formula, we get:

c=(-2±√(2^2-4(6)(-12)))/(2(6))

Simplifying:

c=(-2±√(4+288))/(12)

c=(-2±√292)/(12)

c=(-2±2√73)/(12)

Therefore, the solutions to the equation are c=(-1±√73)/6.