Solve -507=(n-2)(-4n-10)/2

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

n_{1} = - \frac{1 + 4137}{4}, n_{2} = \frac{- 1 + 4137}{4}

Alternative Form

n_{1} \approx - 16.329879, n_{2} \approx 15.829879

Evaluate

- 507 = (n - 2) \times \frac{- 4 n - 10}{2}

Divide the terms

More Steps

- 507 = (n - 2) (- 2 n - 5)

Swap the sides

(n - 2) (- 2 n - 5) = - 507

Expand the expression

More Steps

- 2 n^{2} - n + 10 = - 507

Move the expression to the left side

- 2 n^{2} - n + 517 = 0

Multiply both sides

2 n^{2} + n - 517 = 0

Substitute a= 2,b= 1 and c= - 517 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{- 1 \pm 1 ^{2} - 4 \times 2 ( - 517 )}{2 \times 2}

Simplify the expression

n = \frac{- 1 \pm 1 ^{2} - 4 \times 2 ( - 517 )}{4}

Simplify the expression

More Steps

n = \frac{- 1 \pm 4137}{4}

Separate the equation into 2 possible cases

n = \frac{- 1 + 4137}{4} n = \frac{- 1 - 4137}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

n = \frac{- 1 + 4137}{4} n = - \frac{1 + 4137}{4}

Solution

n_{1} = - \frac{1 + 4137}{4}, n_{2} = \frac{- 1 + 4137}{4}

Alternative Form

n_{1} \approx - 16.329879, n_{2} \approx 15.829879

Show Solution