What are the solutions to the equation v^2-12v-81=-9 ?

The solutions to the equation v^2-12v-81=-9 are v=6(1+sqrt(3)),v=6(1-sqrt(3))

Find the zeros of v^2-12v-81=-9

The zeros of v^2-12v-81=-9 are v=6(1+sqrt(3)),v=6(1-sqrt(3))

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v^{2} - 12 v - 81 = - 9

v = 6 (1 + 3), v = 6 (1 - 3)

Decimal Notation

v = 16.39230 \dots, v = - 4.39230 \dots

Solution steps

v^{2} - 12 v - 81 = - 9

Move

9

to the left side

v^{2} - 12 v - 72 = 0

Solve with the quadratic formula

v_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 1 \cdot ( - 72 )}{2 \cdot 1}

(- 12)^{2} - 4 \cdot 1 \cdot (- 72) = 123

v_{1, 2} = \frac{- ( - 12 ) \pm 12 3}{2 \cdot 1}

Separate the solutions

v_{1} = \frac{- ( - 12 ) + 12 3}{2 \cdot 1}, v_{2} = \frac{- ( - 12 ) - 12 3}{2 \cdot 1}

v = \frac{- ( - 12 ) + 12 3}{2 \cdot 1} : 6 (1 + 3)

v = \frac{- ( - 12 ) - 12 3}{2 \cdot 1} : 6 (1 - 3)

The solutions to the quadratic equation are:

v = 6 (1 + 3), v = 6 (1 - 3)

x, y = 18 - \frac{1}{8} x^{2}

0 = x^{2} - 11 x + 30

3 f^{2} - 16 f + 16 = 0

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

0 = - x^{2} + 8 x - 15

What are the solutions to the equation v^2-12v-81=-9 ?
The solutions to the equation v^2-12v-81=-9 are v=6(1+sqrt(3)),v=6(1-sqrt(3))
Find the zeros of v^2-12v-81=-9
The zeros of v^2-12v-81=-9 are v=6(1+sqrt(3)),v=6(1-sqrt(3))