What are the solutions to the equation -0.5a^2+243a-3280.5=0 ?

The solutions to the equation -0.5a^2+243a-3280.5=0 are a=81(3-2sqrt(2)),a=81(3+2sqrt(2))

Find the zeros of -0.5a^2+243a-3280.5=0

The zeros of -0.5a^2+243a-3280.5=0 are a=81(3-2sqrt(2)),a=81(3+2sqrt(2))

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- 0.5 a^{2} + 243 a - 3280.5 = 0

a = 81 (3 - 22), a = 81 (3 + 22)

Decimal Notation

a = 13.89740 \dots, a = 472.10259 \dots

Solution steps

- 0.5 a^{2} + 243 a - 3280.5 = 0

Multiply both sides by

10

- 5 a^{2} + 2430 a - 32805 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- 2430 \pm 243 0 ^{2} - 4 ( - 5 ) ( - 32805 )}{2 ( - 5 )}

243 0^{2} - 4 (- 5) (- 32805) = 16202

a_{1, 2} = \frac{- 2430 \pm 1620 2}{2 ( - 5 )}

Separate the solutions

a_{1} = \frac{- 2430 + 1620 2}{2 ( - 5 )}, a_{2} = \frac{- 2430 - 1620 2}{2 ( - 5 )}

a = \frac{- 2430 + 1620 2}{2 ( - 5 )} : 81 (3 - 22)

a = \frac{- 2430 - 1620 2}{2 ( - 5 )} : 81 (3 + 22)

The solutions to the quadratic equation are:

a = 81 (3 - 22), a = 81 (3 + 22)

2 a - 4 x = x^{2} + a^{2} - 4

0.0493 x^{2} - 0.9621 x + 53.104 - 70 = 0

(2 x + 1)^{2} = 1 + (x + 1) (x - 1)

x^{2} - 2 x + 6

4 x^{2} - 13 = 9 x

What are the solutions to the equation -0.5a^2+243a-3280.5=0 ?
The solutions to the equation -0.5a^2+243a-3280.5=0 are a=81(3-2sqrt(2)),a=81(3+2sqrt(2))
Find the zeros of -0.5a^2+243a-3280.5=0
The zeros of -0.5a^2+243a-3280.5=0 are a=81(3-2sqrt(2)),a=81(3+2sqrt(2))