What are the solutions to the equation 8x-2x^2=1 ?

The solutions to the equation 8x-2x^2=1 are x=(4-sqrt(14))/2 ,x=(4+sqrt(14))/2

Find the zeros of 8x-2x^2=1

The zeros of 8x-2x^2=1 are x=(4-sqrt(14))/2 ,x=(4+sqrt(14))/2

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8 x - 2 x^{2} = 1

x = \frac{4 - 14}{2}, x = \frac{4 + 14}{2}

Decimal Notation

x = 0.12917 \dots, x = 3.87082 \dots

Solution steps

8 x - 2 x^{2} = 1

Move

1

to the left side

8 x - 2 x^{2} - 1 = 0

Write in the standard form

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

- 2 x^{2} + 8 x - 1 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{4 - 14}{2}, x = \frac{4 + 14}{2}

x^{2} + 25 = 0

3 (x - 7)^{2} + 16 = 46

x^{2} - 4 x + 20

2 x^{2} - 100 = x^{2} - 19

3 (x + 5)^{2} - 13 = - 1

What are the solutions to the equation 8x-2x^2=1 ?
The solutions to the equation 8x-2x^2=1 are x=(4-sqrt(14))/2 ,x=(4+sqrt(14))/2
Find the zeros of 8x-2x^2=1
The zeros of 8x-2x^2=1 are x=(4-sqrt(14))/2 ,x=(4+sqrt(14))/2