Solve 108=180x^2-360x

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{5 - 2 10}{5}, x_{2} = \frac{5 + 2 10}{5}

Alternative Form

x_{1} \approx - 0.264911, x_{2} \approx 2.264911

Evaluate

108 = 180 x^{2} - 360 x

Swap the sides

180 x^{2} - 360 x = 108

Move the expression to the left side

180 x^{2} - 360 x - 108 = 0

Substitute a= 180,b= - 360 and c= - 108 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{360 \pm ( - 360 ) ^{2} - 4 \times 180 ( - 108 )}{2 \times 180}

Simplify the expression

x = \frac{360 \pm ( - 360 ) ^{2} - 4 \times 180 ( - 108 )}{360}

Simplify the expression

More Steps

x = \frac{360 \pm 36 0 ^{2} + 77760}{360}

Simplify the radical expression

More Steps

x = \frac{360 \pm 144 10}{360}

Separate the equation into 2 possible cases

x = \frac{360 + 144 10}{360} x = \frac{360 - 144 10}{360}

Simplify the expression

More Steps

x = \frac{5 + 2 10}{5} x = \frac{360 - 144 10}{360}

Simplify the expression

More Steps

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

Solution

x_{1} = \frac{5 - 2 10}{5}, x_{2} = \frac{5 + 2 10}{5}

Alternative Form

x_{1} \approx - 0.264911, x_{2} \approx 2.264911

Show Solution