What are the solutions to the equation (x+5)(x-6)=1 ?

The solutions to the equation (x+5)(x-6)=1 are x=(1+5sqrt(5))/2 ,x=(1-5sqrt(5))/2

Find the zeros of (x+5)(x-6)=1

The zeros of (x+5)(x-6)=1 are x=(1+5sqrt(5))/2 ,x=(1-5sqrt(5))/2

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(x + 5) (x - 6) = 1

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

Decimal Notation

x = 6.09016 \dots, x = - 5.09016 \dots

Solution steps

(x + 5) (x - 6) = 1

Expand

(x + 5) (x - 6) : x^{2} - x - 30

x^{2} - x - 30 = 1

Move

1

to the left side

x^{2} - x - 31 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot ( - 31 )}{2 \cdot 1}

(- 1)^{2} - 4 \cdot 1 \cdot (- 31) = 55

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

3 x^{2} - 14 x - 13 = 2 x^{2}

x^{2} - 3 x = 3 x^{2} - 5 x - 24

x^{2} + (x - 8)^{2} - 10 = (3 x - 1) (x - 5)

3 x^{2} - 100 x + 750 = 0

(x + 4) (x + 6) = 8

What are the solutions to the equation (x+5)(x-6)=1 ?
The solutions to the equation (x+5)(x-6)=1 are x=(1+5sqrt(5))/2 ,x=(1-5sqrt(5))/2
Find the zeros of (x+5)(x-6)=1
The zeros of (x+5)(x-6)=1 are x=(1+5sqrt(5))/2 ,x=(1-5sqrt(5))/2