Solve 1000x^2-20x-3=0

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{1 - 31}{100}, x_{2} = \frac{1 + 31}{100}

Alternative Form

x_{1} \approx - 0.045678, x_{2} \approx 0.065678

Evaluate

1000 x^{2} - 20 x - 3 = 0

Substitute a= 1000,b= - 20 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 1000 ( - 3 )}{2 \times 1000}

Simplify the expression

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 1000 ( - 3 )}{2000}

Simplify the expression

More Steps

x = \frac{20 \pm 12400}{2000}

Simplify the radical expression

More Steps

x = \frac{20 \pm 20 31}{2000}

Separate the equation into 2 possible cases

x = \frac{20 + 20 31}{2000} x = \frac{20 - 20 31}{2000}

Simplify the expression

More Steps

x = \frac{1 + 31}{100} x = \frac{20 - 20 31}{2000}

Simplify the expression

More Steps

x = \frac{1 + 31}{100} x = \frac{1 - 31}{100}

Solution

x_{1} = \frac{1 - 31}{100}, x_{2} = \frac{1 + 31}{100}

Alternative Form

x_{1} \approx - 0.045678, x_{2} \approx 0.065678

Show Solution