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

The solutions to the equation 4x^2+2x=1 are x=(-1+sqrt(5))/4 ,x=-(1+sqrt(5))/4

Find the zeros of 4x^2+2x=1

The zeros of 4x^2+2x=1 are x=(-1+sqrt(5))/4 ,x=-(1+sqrt(5))/4

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4 x^{2} + 2 x = 1

x = \frac{- 1 + 5}{4}, x = - \frac{1 + 5}{4}

Decimal Notation

x = 0.30901 \dots, x = - 0.80901 \dots

Solution steps

4 x^{2} + 2 x = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

2^{2} - 4 \cdot 4 (- 1) = 25

x_{1, 2} = \frac{- 2 \pm 2 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- 2 + 2 5}{2 \cdot 4}, x_{2} = \frac{- 2 - 2 5}{2 \cdot 4}

x = \frac{- 2 + 2 5}{2 \cdot 4} : \frac{- 1 + 5}{4}

x = \frac{- 2 - 2 5}{2 \cdot 4} : - \frac{1 + 5}{4}

The solutions to the quadratic equation are:

x = \frac{- 1 + 5}{4}, x = - \frac{1 + 5}{4}

0 = 50 + 20 \cdot t - 5 \cdot t^{2}

t^{2} - 4 t - 4 = 0

(2 a + 1) (a - 1) = (3 a - 2) (2 a - 4)

- 2 x^{2} + 4 x + 11 = 0

p^{2} + 14 p - 38

What are the solutions to the equation 4x^2+2x=1 ?
The solutions to the equation 4x^2+2x=1 are x=(-1+sqrt(5))/4 ,x=-(1+sqrt(5))/4
Find the zeros of 4x^2+2x=1
The zeros of 4x^2+2x=1 are x=(-1+sqrt(5))/4 ,x=-(1+sqrt(5))/4