Solve 100x^2-100x-11=9

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{5 - 3 5}{10}, x_{2} = \frac{5 + 3 5}{10}

Alternative Form

x_{1} \approx - 0.17082, x_{2} \approx 1.17082

Evaluate

100 x^{2} - 100 x - 11 = 9

Move the expression to the left side

100 x^{2} - 100 x - 20 = 0

Substitute a= 100,b= - 100 and c= - 20 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{100 \pm ( - 100 ) ^{2} - 4 \times 100 ( - 20 )}{2 \times 100}

Simplify the expression

x = \frac{100 \pm ( - 100 ) ^{2} - 4 \times 100 ( - 20 )}{200}

Simplify the expression

More Steps

x = \frac{100 \pm 18000}{200}

Simplify the radical expression

More Steps

x = \frac{100 \pm 60 5}{200}

Separate the equation into 2 possible cases

x = \frac{100 + 60 5}{200} x = \frac{100 - 60 5}{200}

Simplify the expression

More Steps

x = \frac{5 + 3 5}{10} x = \frac{100 - 60 5}{200}

Simplify the expression

More Steps

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

Solution

x_{1} = \frac{5 - 3 5}{10}, x_{2} = \frac{5 + 3 5}{10}

Alternative Form

x_{1} \approx - 0.17082, x_{2} \approx 1.17082

Show Solution