Solve 4n-40=7(-2n^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 + 141}{7}, n_{2} = \frac{- 1 + 141}{7}

Alternative Form

n_{1} \approx - 1.839192, n_{2} \approx 1.553477

Evaluate

4 n - 40 = 7 (- 2 n^{2})

Multiply the numbers

More Steps

4 n - 40 = - 14 n^{2}

Swap the sides

- 14 n^{2} = 4 n - 40

Move the expression to the left side

- 14 n^{2} - 4 n + 40 = 0

Multiply both sides

14 n^{2} + 4 n - 40 = 0

Substitute a= 14,b= 4 and c= - 40 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{- 4 \pm 4 ^{2} - 4 \times 14 ( - 40 )}{2 \times 14}

Simplify the expression

n = \frac{- 4 \pm 4 ^{2} - 4 \times 14 ( - 40 )}{28}

Simplify the expression

More Steps

n = \frac{- 4 \pm 2256}{28}

Simplify the radical expression

More Steps

n = \frac{- 4 \pm 4 141}{28}

Separate the equation into 2 possible cases

n = \frac{- 4 + 4 141}{28} n = \frac{- 4 - 4 141}{28}

Simplify the expression

More Steps

n = \frac{- 1 + 141}{7} n = \frac{- 4 - 4 141}{28}

Simplify the expression

More Steps

n = \frac{- 1 + 141}{7} n = - \frac{1 + 141}{7}

Solution

n_{1} = - \frac{1 + 141}{7}, n_{2} = \frac{- 1 + 141}{7}

Alternative Form

n_{1} \approx - 1.839192, n_{2} \approx 1.553477

Show Solution