What are the solutions to the equation x^2-ax-1=0 ?

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

Find the zeros of x^2-ax-1=0

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

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x^{2} - a x - 1 = 0

x = \frac{a + a ^{2} + 4}{2}, x = \frac{a - a ^{2} + 4}{2}

Solution steps

x^{2} - a x - 1 = 0

Solve with the quadratic formula

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

Simplify

(- a)^{2} - 4 \cdot 1 \cdot (- 1) : a^{2} + 4

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{a + a ^{2} + 4}{2}, x = \frac{a - a ^{2} + 4}{2}

(7 x - 1)^{2} = 1

4 x^{2} - 24 x + 27

4 x^{2} + 8 x - 9

3 x^{2} + 6 x = 72

2 (x - 3)^{2} + 1 = 101

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