Solve for x 6x^2-144x+486=0

Problem

6*x2−144*x+486=0

Solution

1. Divide the entire equation by the greatest common factor, which is 6 to simplify the coefficients.

x2−24*x+81=0

2. Identify two numbers that multiply to 81 and add to −24 to factor the quadratic expression.

−21×−3=63

−27×−3=81

−27+(−3)=−30

Wait, let's re-examine the factors of 81 The factors are (1,81) (3,27) and (9,9)
Since −21 and −3 do not work, we check 3 and 27

−3+(−27)=−30

Let's use the Quadratic Formula instead: x=(−b±√(,b2−4*a*c))/(2*a) where a=1 b=−24 and c=81

x=(24±√(,(−24)2−4*(1)*(81)))/(2*(1))

3. Calculate the discriminant inside the square root.

24=576

4×81=324

576−324=252

4. Simplify the square root of the discriminant.

√(,252)=√(,36×7)

√(,252)=6√(,7)

5. Substitute back into the formula to find the values of x

x=(24±6√(,7))/2

x=12±3√(,7)

Final Answer

x=12±3√(,7)

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