Solve (x-1)/2 (x-3)/3=6

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 2 - 37, x_{2} = 2 + 37

Alternative Form

x_{1} \approx - 4.082763, x_{2} \approx 8.082763

Evaluate

\frac{x - 1}{2} \times \frac{x - 3}{3} = 6

Multiply the terms

More Steps

\frac{( x - 1 ) ( x - 3 )}{6} = 6

Rewrite the expression

\frac{1}{6} x^{2} - \frac{2}{3} x + \frac{1}{2} = 6

Move the expression to the left side

\frac{1}{6} x^{2} - \frac{2}{3} x - \frac{11}{2} = 0

Multiply both sides

6 (\frac{1}{6} x^{2} - \frac{2}{3} x - \frac{11}{2}) = 6 \times 0

Calculate

x^{2} - 4 x - 33 = 0

Substitute a= 1,b= - 4 and c= - 33 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{4 \pm ( - 4 ) ^{2} - 4 ( - 33 )}{2}

Simplify the expression

More Steps

x = \frac{4 \pm 148}{2}

Simplify the radical expression

More Steps

x = \frac{4 \pm 2 37}{2}

Separate the equation into 2 possible cases

x = \frac{4 + 2 37}{2} x = \frac{4 - 2 37}{2}

Simplify the expression

More Steps

x = 2 + 37 x = \frac{4 - 2 37}{2}

Simplify the expression

More Steps

x = 2 + 37 x = 2 - 37

Solution

x_{1} = 2 - 37, x_{2} = 2 + 37

Alternative Form

x_{1} \approx - 4.082763, x_{2} \approx 8.082763

Show Solution