What are the solutions to the equation (x-6)^2+x^2-6x-2=0 ?

The solutions to the equation (x-6)^2+x^2-6x-2=0 are x=(9+sqrt(13))/2 ,x=(9-sqrt(13))/2

Find the zeros of (x-6)^2+x^2-6x-2=0

The zeros of (x-6)^2+x^2-6x-2=0 are x=(9+sqrt(13))/2 ,x=(9-sqrt(13))/2

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(x - 6)^{2} + x^{2} - 6 x - 2 = 0

x = \frac{9 + 13}{2}, x = \frac{9 - 13}{2}

Decimal Notation

x = 6.30277 \dots, x = 2.69722 \dots

Solution steps

(x - 6)^{2} + x^{2} - 6 x - 2 = 0

Expand

(x - 6)^{2} + x^{2} - 6 x - 2 : 2 x^{2} - 18 x + 34

2 x^{2} - 18 x + 34 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 2 \cdot 34}{2 \cdot 2}

(- 18)^{2} - 4 \cdot 2 \cdot 34 = 213

x_{1, 2} = \frac{- ( - 18 ) \pm 2 13}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 2 13}{2 \cdot 2}, x_{2} = \frac{- ( - 18 ) - 2 13}{2 \cdot 2}

x = \frac{- ( - 18 ) + 2 13}{2 \cdot 2} : \frac{9 + 13}{2}

x = \frac{- ( - 18 ) - 2 13}{2 \cdot 2} : \frac{9 - 13}{2}

The solutions to the quadratic equation are:

x = \frac{9 + 13}{2}, x = \frac{9 - 13}{2}

\frac{( 2 + 4 - 3 ) ^{2} - 1}{- 4}

x^{2} - 147 = 0

(\frac{1}{16})^{\frac{5}{4}}

e^{- x} e^{- x}

4 m^{2} + 10 m + 4

What are the solutions to the equation (x-6)^2+x^2-6x-2=0 ?
The solutions to the equation (x-6)^2+x^2-6x-2=0 are x=(9+sqrt(13))/2 ,x=(9-sqrt(13))/2
Find the zeros of (x-6)^2+x^2-6x-2=0
The zeros of (x-6)^2+x^2-6x-2=0 are x=(9+sqrt(13))/2 ,x=(9-sqrt(13))/2