Solve 50 = ((2x-20) (x))/2

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = 5 - 53, x_{2} = 5 + 53

Alternative Form

x_{1} \approx - 3.660254, x_{2} \approx 13.660254

Evaluate

50 = \frac{( 2 x - 20 ) x}{2}

Simplify

More Steps

50 = x (x - 10)

Swap the sides

x (x - 10) = 50

Expand the expression

More Steps

x^{2} - 10 x = 50

Move the expression to the left side

x^{2} - 10 x - 50 = 0

Substitute a= 1,b= - 10 and c= - 50 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{10 \pm ( - 10 ) ^{2} - 4 ( - 50 )}{2}

Simplify the expression

More Steps

x = \frac{10 \pm 300}{2}

Simplify the radical expression

More Steps

x = \frac{10 \pm 10 3}{2}

Separate the equation into 2 possible cases

x = \frac{10 + 10 3}{2} x = \frac{10 - 10 3}{2}

Simplify the expression

More Steps

x = 5 + 53 x = \frac{10 - 10 3}{2}

Simplify the expression

More Steps

x = 5 + 53 x = 5 - 53

Solution

x_{1} = 5 - 53, x_{2} = 5 + 53

Alternative Form

x_{1} \approx - 3.660254, x_{2} \approx 13.660254

Show Solution