What are the solutions to the equation 4x^2-4x-7=0 ?

The solutions to the equation 4x^2-4x-7=0 are x=(1+2sqrt(2))/2 ,x=(1-2sqrt(2))/2

Find the zeros of 4x^2-4x-7=0

The zeros of 4x^2-4x-7=0 are x=(1+2sqrt(2))/2 ,x=(1-2sqrt(2))/2

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4 x^{2} - 4 x - 7 = 0

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

Decimal Notation

x = 1.91421 \dots, x = - 0.91421 \dots

Solution steps

4 x^{2} - 4 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 4 ( - 7 )}{2 \cdot 4}

(- 4)^{2} - 4 \cdot 4 (- 7) = 82

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

Separate the solutions

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

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

x = \frac{- ( - 4 ) - 8 2}{2 \cdot 4} : \frac{1 - 2 2}{2}

The solutions to the quadratic equation are:

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

3 x^{2} - 5 x + 2 = 0

- 8 x^{2} + 46 x - 30 = 0

2 x^{2} - 24 x = - 72

- 2 x^{2} + 6 x - 10 = - 3 x^{2}

16 x^{2} + 8 x - 3 = 0

What are the solutions to the equation 4x^2-4x-7=0 ?
The solutions to the equation 4x^2-4x-7=0 are x=(1+2sqrt(2))/2 ,x=(1-2sqrt(2))/2
Find the zeros of 4x^2-4x-7=0
The zeros of 4x^2-4x-7=0 are x=(1+2sqrt(2))/2 ,x=(1-2sqrt(2))/2