What are the solutions to the equation (x+5)(x-5)-5(x-4)=(x-4) ?

The solutions to the equation (x+5)(x-5)-5(x-4)=(x-4) are x=3+sqrt(10),x=3-sqrt(10)

Find the zeros of (x+5)(x-5)-5(x-4)=(x-4)

The zeros of (x+5)(x-5)-5(x-4)=(x-4) are x=3+sqrt(10),x=3-sqrt(10)

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(x + 5) (x - 5) - 5 (x - 4) = (x - 4)

x = 3 + 10, x = 3 - 10

Decimal Notation

x = 6.16227 \dots, x = - 0.16227 \dots

Solution steps

(x + 5) (x - 5) - 5 (x - 4) = (x - 4)

Expand

(x + 5) (x - 5) - 5 (x - 4) : x^{2} - 5 x - 5

x^{2} - 5 x - 5 = x - 4

Move

4

to the left side

x^{2} - 5 x - 1 = x

Move

x

to the left side

x^{2} - 6 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot (- 1) = 210

x_{1, 2} = \frac{- ( - 6 ) \pm 2 10}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 10}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 2 10}{2 \cdot 1}

x = \frac{- ( - 6 ) + 2 10}{2 \cdot 1} : 3 + 10

x = \frac{- ( - 6 ) - 2 10}{2 \cdot 1} : 3 - 10

The solutions to the quadratic equation are:

x = 3 + 10, x = 3 - 10

x^{2} + 0.4 x + 4.04 = 0

2 r^{2} + 8 r + 6 = 0

x (x - 2) = 3

(x) = 0.3 x^{2} - 144 x + 30178

3 x^{2} + 7 x = 4

What are the solutions to the equation (x+5)(x-5)-5(x-4)=(x-4) ?
The solutions to the equation (x+5)(x-5)-5(x-4)=(x-4) are x=3+sqrt(10),x=3-sqrt(10)
Find the zeros of (x+5)(x-5)-5(x-4)=(x-4)
The zeros of (x+5)(x-5)-5(x-4)=(x-4) are x=3+sqrt(10),x=3-sqrt(10)