Solve x1 (x1-6)/3=42

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 3 - 315, x_{2} = 3 + 315

Alternative Form

x_{1} \approx - 8.61895, x_{2} \approx 14.61895

Evaluate

x (1 \times \frac{x \times 1 - 6}{3}) = 42

Remove the parentheses

x \times 1 \times \frac{x \times 1 - 6}{3} = 42

Simplify

More Steps

\frac{x ( x - 6 )}{3} = 42

Rewrite the expression

\frac{1}{3} x^{2} - 2 x = 42

Move the expression to the left side

\frac{1}{3} x^{2} - 2 x - 42 = 0

Multiply both sides

3 (\frac{1}{3} x^{2} - 2 x - 42) = 3 \times 0

Calculate

x^{2} - 6 x - 126 = 0

Substitute a= 1,b= - 6 and c= - 126 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 ( - 126 )}{2}

Simplify the expression

More Steps

x = \frac{6 \pm 540}{2}

Simplify the radical expression

More Steps

x = \frac{6 \pm 6 15}{2}

Separate the equation into 2 possible cases

x = \frac{6 + 6 15}{2} x = \frac{6 - 6 15}{2}

Simplify the expression

More Steps

x = 3 + 315 x = \frac{6 - 6 15}{2}

Simplify the expression

More Steps

x = 3 + 315 x = 3 - 315

Solution

x_{1} = 3 - 315, x_{2} = 3 + 315

Alternative Form

x_{1} \approx - 8.61895, x_{2} \approx 14.61895

Show Solution