What are the solutions to the equation 1+x-53=x^2-2x-152x ?

The solutions to the equation 1+x-53=x^2-2x-152x are x=(155+sqrt(23817))/2 ,x=(155-sqrt(23817))/2

Find the zeros of 1+x-53=x^2-2x-152x

The zeros of 1+x-53=x^2-2x-152x are x=(155+sqrt(23817))/2 ,x=(155-sqrt(23817))/2

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1 + x - 53 = x^{2} - 2 x - 152 x

x = \frac{155 + 23817}{2}, x = \frac{155 - 23817}{2}

Decimal Notation

x = 154.66378 \dots, x = 0.33621 \dots

Solution steps

1 + x - 53 = x^{2} - 2 x - 152 x

Refine

x - 52 = x^{2} - 154 x

Switch sides

x^{2} - 154 x = x - 52

Move

52

to the left side

x^{2} - 154 x + 52 = x

Move

x

to the left side

x^{2} - 155 x + 52 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 155 ) \pm ( - 155 ) ^{2} - 4 \cdot 1 \cdot 52}{2 \cdot 1}

(- 155)^{2} - 4 \cdot 1 \cdot 52 = 23817

x_{1, 2} = \frac{- ( - 155 ) \pm 23817}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 155 ) + 23817}{2 \cdot 1}, x_{2} = \frac{- ( - 155 ) - 23817}{2 \cdot 1}

x = \frac{- ( - 155 ) + 23817}{2 \cdot 1} : \frac{155 + 23817}{2}

x = \frac{- ( - 155 ) - 23817}{2 \cdot 1} : \frac{155 - 23817}{2}

The solutions to the quadratic equation are:

x = \frac{155 + 23817}{2}, x = \frac{155 - 23817}{2}

- 16 x > - 80

6 x^{2} + 48 x

x + 3 < 12

9 u - 27

y = y^{2} - 4

What are the solutions to the equation 1+x-53=x^2-2x-152x ?
The solutions to the equation 1+x-53=x^2-2x-152x are x=(155+sqrt(23817))/2 ,x=(155-sqrt(23817))/2
Find the zeros of 1+x-53=x^2-2x-152x
The zeros of 1+x-53=x^2-2x-152x are x=(155+sqrt(23817))/2 ,x=(155-sqrt(23817))/2