What are the solutions to the equation 0=-1/4 x^2+4x-1 ?

The solutions to the equation 0=-1/4 x^2+4x-1 are x=2(4-sqrt(15)),x=2(4+sqrt(15))

Find the zeros of 0=-1/4 x^2+4x-1

The zeros of 0=-1/4 x^2+4x-1 are x=2(4-sqrt(15)),x=2(4+sqrt(15))

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0 = - \frac{1}{4} x^{2} + 4 x - 1

x = 2 (4 - 15), x = 2 (4 + 15)

Decimal Notation

x = 0.25403 \dots, x = 15.74596 \dots

Solution steps

0 = - \frac{1}{4} x^{2} + 4 x - 1

Multiply both sides by

4

0 = - x^{2} + 16 x - 4

Switch sides

- x^{2} + 16 x - 4 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 ( - 1 ) ( - 4 )}{2 ( - 1 )}

1 6^{2} - 4 (- 1) (- 4) = 415

x_{1, 2} = \frac{- 16 \pm 4 15}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 16 + 4 15}{2 ( - 1 )}, x_{2} = \frac{- 16 - 4 15}{2 ( - 1 )}

x = \frac{- 16 + 4 15}{2 ( - 1 )} : 2 (4 - 15)

x = \frac{- 16 - 4 15}{2 ( - 1 )} : 2 (4 + 15)

The solutions to the quadratic equation are:

x = 2 (4 - 15), x = 2 (4 + 15)

2 x - 3 = 1 - 2 x + x^{2}

- 10 x^{2} + 1760 x - 5000 = 72440

4 x^{2} - x - 9 = - x - 8

- 0.0006 t^{2} + 0.048 t - 0.29 = 0

x, 2 x^{2} - 5 x - 4 = 0

What are the solutions to the equation 0=-1/4 x^2+4x-1 ?
The solutions to the equation 0=-1/4 x^2+4x-1 are x=2(4-sqrt(15)),x=2(4+sqrt(15))
Find the zeros of 0=-1/4 x^2+4x-1
The zeros of 0=-1/4 x^2+4x-1 are x=2(4-sqrt(15)),x=2(4+sqrt(15))