What are the solutions to the equation 4x^2-19=-4x ?

The solutions to the equation 4x^2-19=-4x are x=(-1+2sqrt(5))/2 ,x=-(1+2sqrt(5))/2

Find the zeros of 4x^2-19=-4x

The zeros of 4x^2-19=-4x are x=(-1+2sqrt(5))/2 ,x=-(1+2sqrt(5))/2

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4 x^{2} - 19 = - 4 x

x = \frac{- 1 + 2 5}{2}, x = - \frac{1 + 2 5}{2}

Decimal Notation

x = 1.73606 \dots, x = - 2.73606 \dots

Solution steps

4 x^{2} - 19 = - 4 x

Move

4 x

to the left side

4 x^{2} - 19 + 4 x = 0

Write in the standard form

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

4 x^{2} + 4 x - 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 4 ( - 19 )}{2 \cdot 4}

4^{2} - 4 \cdot 4 (- 19) = 85

x_{1, 2} = \frac{- 4 \pm 8 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- 4 + 8 5}{2 \cdot 4}, x_{2} = \frac{- 4 - 8 5}{2 \cdot 4}

x = \frac{- 4 + 8 5}{2 \cdot 4} : \frac{- 1 + 2 5}{2}

x = \frac{- 4 - 8 5}{2 \cdot 4} : - \frac{1 + 2 5}{2}

The solutions to the quadratic equation are:

x = \frac{- 1 + 2 5}{2}, x = - \frac{1 + 2 5}{2}

3 x^{2} - 3 = 1

17 - 2 x^{2} = - 21

19 - 3 x^{2} = - 8

(x + 7)^{2} - 23 = 34

5 x^{2} - 11 = 234

What are the solutions to the equation 4x^2-19=-4x ?
The solutions to the equation 4x^2-19=-4x are x=(-1+2sqrt(5))/2 ,x=-(1+2sqrt(5))/2
Find the zeros of 4x^2-19=-4x
The zeros of 4x^2-19=-4x are x=(-1+2sqrt(5))/2 ,x=-(1+2sqrt(5))/2