What are the solutions to the equation r^2-r-11=0 ?

The solutions to the equation r^2-r-11=0 are r=(1+3sqrt(5))/2 ,r=(1-3sqrt(5))/2

Find the zeros of r^2-r-11=0

The zeros of r^2-r-11=0 are r=(1+3sqrt(5))/2 ,r=(1-3sqrt(5))/2

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r^{2} - r - 11 = 0

r = \frac{1 + 3 5}{2}, r = \frac{1 - 3 5}{2}

Decimal Notation

r = 3.85410 \dots, r = - 2.85410 \dots

Solution steps

r^{2} - r - 11 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot ( - 11 )}{2 \cdot 1}

(- 1)^{2} - 4 \cdot 1 \cdot (- 11) = 35

r_{1, 2} = \frac{- ( - 1 ) \pm 3 5}{2 \cdot 1}

Separate the solutions

r_{1} = \frac{- ( - 1 ) + 3 5}{2 \cdot 1}, r_{2} = \frac{- ( - 1 ) - 3 5}{2 \cdot 1}

r = \frac{- ( - 1 ) + 3 5}{2 \cdot 1} : \frac{1 + 3 5}{2}

r = \frac{- ( - 1 ) - 3 5}{2 \cdot 1} : \frac{1 - 3 5}{2}

The solutions to the quadratic equation are:

r = \frac{1 + 3 5}{2}, r = \frac{1 - 3 5}{2}

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

2 x^{2} - 28 x = - 76

(2 x + 1)^{2} = 31

3 (x - 1) = 4 x^{2}

(m - 1) x^{2} - 3 m x + m + 1 = 0

What are the solutions to the equation r^2-r-11=0 ?
The solutions to the equation r^2-r-11=0 are r=(1+3sqrt(5))/2 ,r=(1-3sqrt(5))/2
Find the zeros of r^2-r-11=0
The zeros of r^2-r-11=0 are r=(1+3sqrt(5))/2 ,r=(1-3sqrt(5))/2