What are the solutions to the equation (7298-x)^2=x ?

The solutions to the equation (7298-x)^2=x are x=(14597+sqrt(29193))/2 ,x=(14597-sqrt(29193))/2

Find the zeros of (7298-x)^2=x

The zeros of (7298-x)^2=x are x=(14597+sqrt(29193))/2 ,x=(14597-sqrt(29193))/2

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(7298 - x)^{2} = x

x = \frac{14597 + 29193}{2}, x = \frac{14597 - 29193}{2}

Decimal Notation

x = 7383.92979 \dots, x = 7213.07020 \dots

Solution steps

(7298 - x)^{2} = x

Expand

(7298 - x)^{2} : 53260804 - 14596 x + x^{2}

53260804 - 14596 x + x^{2} = x

Move

x

to the left side

x^{2} - 14597 x + 53260804 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 14597 ) \pm ( - 14597 ) ^{2} - 4 \cdot 1 \cdot 53260804}{2 \cdot 1}

(- 14597)^{2} - 4 \cdot 1 \cdot 53260804 = 29193

x_{1, 2} = \frac{- ( - 14597 ) \pm 29193}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 14597 ) + 29193}{2 \cdot 1}, x_{2} = \frac{- ( - 14597 ) - 29193}{2 \cdot 1}

x = \frac{- ( - 14597 ) + 29193}{2 \cdot 1} : \frac{14597 + 29193}{2}

x = \frac{- ( - 14597 ) - 29193}{2 \cdot 1} : \frac{14597 - 29193}{2}

The solutions to the quadratic equation are:

x = \frac{14597 + 29193}{2}, x = \frac{14597 - 29193}{2}

x^{2} - 13 x + 4 = 0

(5 x + 1) (x - 8) = 0

2 = x^{2} - 2

x^{2} - 5 x - 31 = 5

x^{2} - 12 = - 3

What are the solutions to the equation (7298-x)^2=x ?
The solutions to the equation (7298-x)^2=x are x=(14597+sqrt(29193))/2 ,x=(14597-sqrt(29193))/2
Find the zeros of (7298-x)^2=x
The zeros of (7298-x)^2=x are x=(14597+sqrt(29193))/2 ,x=(14597-sqrt(29193))/2