Solve (4-x)(2-x)=2

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

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

Alternative Form

x_{1} \approx 1.267949, x_{2} \approx 4.732051

Evaluate

(4 - x) (2 - x) = 2

Expand the expression

More Steps

8 - 6 x + x^{2} = 2

Move the expression to the left side

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

Rewrite in standard form

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

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

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

Simplify the expression

More Steps

x = \frac{6 \pm 12}{2}

Simplify the radical expression

More Steps

x = \frac{6 \pm 2 3}{2}

Separate the equation into 2 possible cases

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

Simplify the expression

More Steps

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

Simplify the expression

More Steps

x = 3 + 3 x = 3 - 3

Solution

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

Alternative Form

x_{1} \approx 1.267949, x_{2} \approx 4.732051

Show Solution