What are the solutions to the equation 0.5(x^2+1)=x ?

The solutions to the equation 0.5(x^2+1)=x are x=1

Find the zeros of 0.5(x^2+1)=x

The zeros of 0.5(x^2+1)=x are x=1

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

x = 1

Solution steps

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

Multiply both sides by

10

5 (x^{2} + 1) = x \cdot 10

Expand

5 (x^{2} + 1) : 5 x^{2} + 5

5 x^{2} + 5 = x \cdot 10

Move

x 10

to the left side

5 x^{2} + 5 - x \cdot 10 = 0

Write in the standard form

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

5 x^{2} - 10 x + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 \cdot 5 \cdot 5}{2 \cdot 5}

(- 10)^{2} - 4 \cdot 5 \cdot 5 = 0

x_{1, 2} = \frac{- ( - 10 ) \pm 0}{2 \cdot 5}

x = \frac{- ( - 10 )}{2 \cdot 5}

\frac{- ( - 10 )}{2 \cdot 5} = 1

x = 1

The solution to the quadratic equation is:

x = 1

- x^{2} + x + 7 = 0

x^{2} + 12 x + 36 = 0

- y^{2} = 1

x, x^{2} + y^{2} + 20 x + 2 y + 102 = 0

x^{2} + 4 x + 3 x = 0

What are the solutions to the equation 0.5(x^2+1)=x ?
The solutions to the equation 0.5(x^2+1)=x are x=1
Find the zeros of 0.5(x^2+1)=x
The zeros of 0.5(x^2+1)=x are x=1