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

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

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

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

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4 x^{2} = 1 - 2 x

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} = 1 - 2 x

Move

2 x

to the left side

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}

6 x^{2} - 12 x + 8 = 0

x^{2} - 64 = 0

4 x^{2} + 12 x

6 x^{2} = - 19 x - 15

25 x^{2} + 4 = 20 x

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