What are the solutions to the equation 4a-(a^2)/2 =1 ?

The solutions to the equation 4a-(a^2)/2 =1 are a=4-sqrt(14),a=4+sqrt(14)

Find the zeros of 4a-(a^2)/2 =1

The zeros of 4a-(a^2)/2 =1 are a=4-sqrt(14),a=4+sqrt(14)

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4 a - \frac{a ^{2}}{2} = 1

a = 4 - 14, a = 4 + 14

Decimal Notation

a = 0.25834 \dots, a = 7.74165 \dots

Solution steps

4 a - \frac{a ^{2}}{2} = 1

Multiply both sides by

2

8 a - a^{2} = 2

Move

2

to the left side

8 a - a^{2} - 2 = 0

Write in the standard form

a x^{2} + b x + c = 0

- a^{2} + 8 a - 2 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 ( - 1 ) ( - 2 )}{2 ( - 1 )}

8^{2} - 4 (- 1) (- 2) = 214

a_{1, 2} = \frac{- 8 \pm 2 14}{2 ( - 1 )}

Separate the solutions

a_{1} = \frac{- 8 + 2 14}{2 ( - 1 )}, a_{2} = \frac{- 8 - 2 14}{2 ( - 1 )}

a = \frac{- 8 + 2 14}{2 ( - 1 )} : 4 - 14

a = \frac{- 8 - 2 14}{2 ( - 1 )} : 4 + 14

The solutions to the quadratic equation are:

a = 4 - 14, a = 4 + 14

t^{2} + 9 t + 18

2 x - 1 = x^{2}

3 (2 x + 2) > 24 - 4 x

v^{2} - 49

2^{x + 2} - 2^{x + 1} + 2^{x - 1} - 2^{x - 2} \leq 9

What are the solutions to the equation 4a-(a^2)/2 =1 ?
The solutions to the equation 4a-(a^2)/2 =1 are a=4-sqrt(14),a=4+sqrt(14)
Find the zeros of 4a-(a^2)/2 =1
The zeros of 4a-(a^2)/2 =1 are a=4-sqrt(14),a=4+sqrt(14)