Solve for x 12x^2-136x+289=0

Problem

12*x2−136*x+289=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0

a=12

b=−136

c=289

2. Apply the quadratic formula to find the values of x

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the formula.

x=(−(−136)±√(,(−136)2−4*(12)*(289)))/(2*(12))

4. Calculate the discriminant b2−4*a*c

(−136)2=18496

4*(12)*(289)=13872

18496−13872=4624

5. Simplify the square root of the discriminant.

√(,4624)=68

6. Solve for the two possible values of x

x=(136±68)/24

7. Evaluate the first solution using the plus sign.

(x_1)=(136+68)/24

(x_1)=204/24

(x_1)=17/2

8. Evaluate the second solution using the minus sign.

(x_2)=(136−68)/24

(x_2)=68/24

(x_2)=17/6

Final Answer

x=17/2,17/6

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