Solve n^2-10n 19=6

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

n_{1} = 95 - 9031, n_{2} = 95 + 9031

Alternative Form

n_{1} \approx - 0.031574, n_{2} \approx 190.031574

Evaluate

n^{2} - 10 n \times 19 = 6

Multiply the terms

n^{2} - 190 n = 6

Move the expression to the left side

n^{2} - 190 n - 6 = 0

Substitute a= 1,b= - 190 and c= - 6 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{190 \pm ( - 190 ) ^{2} - 4 ( - 6 )}{2}

Simplify the expression

More Steps

n = \frac{190 \pm 36124}{2}

Simplify the radical expression

More Steps

n = \frac{190 \pm 2 9031}{2}

Separate the equation into 2 possible cases

n = \frac{190 + 2 9031}{2} n = \frac{190 - 2 9031}{2}

Simplify the expression

More Steps

n = 95 + 9031 n = \frac{190 - 2 9031}{2}

Simplify the expression

More Steps

n = 95 + 9031 n = 95 - 9031

Solution

n_{1} = 95 - 9031, n_{2} = 95 + 9031

Alternative Form

n_{1} \approx - 0.031574, n_{2} \approx 190.031574

Show Solution