What are the solutions to the equation 7-x^2=x ?

The solutions to the equation 7-x^2=x are x=-(1+sqrt(29))/2 ,x=(sqrt(29)-1)/2

Find the zeros of 7-x^2=x

The zeros of 7-x^2=x are x=-(1+sqrt(29))/2 ,x=(sqrt(29)-1)/2

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7 - x^{2} = x

x = - \frac{1 + 29}{2}, x = \frac{29 - 1}{2}

Decimal Notation

x = - 3.19258 \dots, x = 2.19258 \dots

Solution steps

7 - x^{2} = x

Move

x

to the left side

7 - x^{2} - x = 0

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 ( - 1 ) \cdot 7}{2 ( - 1 )}

(- 1)^{2} - 4 (- 1) \cdot 7 = 29

x_{1, 2} = \frac{- ( - 1 ) \pm 29}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 29}{2 ( - 1 )}, x_{2} = \frac{- ( - 1 ) - 29}{2 ( - 1 )}

x = \frac{- ( - 1 ) + 29}{2 ( - 1 )} : - \frac{1 + 29}{2}

x = \frac{- ( - 1 ) - 29}{2 ( - 1 )} : \frac{29 - 1}{2}

The solutions to the quadratic equation are:

x = - \frac{1 + 29}{2}, x = \frac{29 - 1}{2}

x^{2} + 22 x = 8 x - 53

\frac{x ( x + 1 )}{2} = 120

x^{2} - 37 x + 27 = 0

7 x^{2} - 66 x + 27 = 0

x^{2} + (x + 5)^{2} = 5 + 16 (3 - x)

What are the solutions to the equation 7-x^2=x ?
The solutions to the equation 7-x^2=x are x=-(1+sqrt(29))/2 ,x=(sqrt(29)-1)/2
Find the zeros of 7-x^2=x
The zeros of 7-x^2=x are x=-(1+sqrt(29))/2 ,x=(sqrt(29)-1)/2