What are the solutions to the equation n^2-14n-83=-6 ?

The solutions to the equation n^2-14n-83=-6 are n=7+3sqrt(14),n=7-3sqrt(14)

Find the zeros of n^2-14n-83=-6

The zeros of n^2-14n-83=-6 are n=7+3sqrt(14),n=7-3sqrt(14)

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n^{2} - 14 n - 83 = - 6

n = 7 + 314, n = 7 - 314

Decimal Notation

n = 18.22497 \dots, n = - 4.22497 \dots

Solution steps

n^{2} - 14 n - 83 = - 6

Move

6

to the left side

n^{2} - 14 n - 77 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 1 \cdot ( - 77 )}{2 \cdot 1}

(- 14)^{2} - 4 \cdot 1 \cdot (- 77) = 614

n_{1, 2} = \frac{- ( - 14 ) \pm 6 14}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- ( - 14 ) + 6 14}{2 \cdot 1}, n_{2} = \frac{- ( - 14 ) - 6 14}{2 \cdot 1}

n = \frac{- ( - 14 ) + 6 14}{2 \cdot 1} : 7 + 314

n = \frac{- ( - 14 ) - 6 14}{2 \cdot 1} : 7 - 314

The solutions to the quadratic equation are:

n = 7 + 314, n = 7 - 314

4 x^{2} = 6 x - 7

24 x^{2} + 10 x - 25 = 0

7 x^{2} + x - 1 = 0

(2 x + 1) \cdot x = 0

0 = x^{2} + 6

What are the solutions to the equation n^2-14n-83=-6 ?
The solutions to the equation n^2-14n-83=-6 are n=7+3sqrt(14),n=7-3sqrt(14)
Find the zeros of n^2-14n-83=-6
The zeros of n^2-14n-83=-6 are n=7+3sqrt(14),n=7-3sqrt(14)