What are the solutions to the equation x^2-2(m-1)x-2m-1=0 ?

The solutions to the equation x^2-2(m-1)x-2m-1=0 are x=m-1+sqrt(m^2+2),x=m-1-sqrt(m^2+2)

Find the zeros of x^2-2(m-1)x-2m-1=0

The zeros of x^2-2(m-1)x-2m-1=0 are x=m-1+sqrt(m^2+2),x=m-1-sqrt(m^2+2)

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

x = m - 1 + m^{2} + 2, x = m - 1 - m^{2} + 2

Solution steps

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

Expand

x^{2} - 2 (m - 1) x - 2 m - 1 : x^{2} - 2 m x + 2 x - 2 m - 1

x^{2} - 2 m x + 2 x - 2 m - 1 = 0

Write in the standard form

a x^{2} + b x + c = 0

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

Solve with the quadratic formula

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

Simplify

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = m - 1 + m^{2} + 2, x = m - 1 - m^{2} + 2

x^{2} - 77 x + 70 = 0

\frac{2}{3} x^{2} = 1 + 5

8 x^{2} - 38 x + 35 = 0

3 X^{2} - 48 = 0

- 6 x^{2} + 9 = - 3 x^{2} + 6

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