Solve (7-x)(3-x)-3=0

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 5 - 7, x_{2} = 5 + 7

Alternative Form

x_{1} \approx 2.354249, x_{2} \approx 7.645751

Evaluate

(7 - x) (3 - x) - 3 = 0

Expand the expression

More Steps

18 - 10 x + x^{2} = 0

Rewrite in standard form

x^{2} - 10 x + 18 = 0

Substitute a= 1,b= - 10 and c= 18 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 18}{2}

Simplify the expression

More Steps

x = \frac{10 \pm 28}{2}

Simplify the radical expression

More Steps

x = \frac{10 \pm 2 7}{2}

Separate the equation into 2 possible cases

x = \frac{10 + 2 7}{2} x = \frac{10 - 2 7}{2}

Simplify the expression

More Steps

x = 5 + 7 x = \frac{10 - 2 7}{2}

Simplify the expression

More Steps

x = 5 + 7 x = 5 - 7

Solution

x_{1} = 5 - 7, x_{2} = 5 + 7

Alternative Form

x_{1} \approx 2.354249, x_{2} \approx 7.645751

Show Solution