Solve for x 0=12x^2-176x+484

Problem

0=12*x2−176*x+484

Solution

1. Divide the entire equation by the greatest common divisor of the coefficients, which is 4 to simplify the quadratic.

0=3*x2−44*x+121

2. Identify the coefficients for the quadratic formula a*x2+b*x+c=0 where a=3 b=−44 and c=121

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the quadratic formula.

x=(−(−44)±√(,(−44)2−4*(3)*(121)))/(2*(3))

4. Calculate the discriminant and the denominator.

x=(44±√(,1936−1452))/6

5. Simplify the expression inside the square root.

x=(44±√(,484))/6

6. Evaluate the square root of 484 which is 22

x=(44±22)/6

7. Solve for the two possible values of x

(x_1)=(44+22)/6=66/6=11

(x_2)=(44−22)/6=22/6=11/3

Final Answer

x=11,11/3

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