What are the solutions to the equation x0.9(x+1)=25+x ?

The solutions to the equation x0.9(x+1)=25+x are x=(1+sqrt(9001))/(18),x=(1-sqrt(9001))/(18)

Find the zeros of x0.9(x+1)=25+x

The zeros of x0.9(x+1)=25+x are x=(1+sqrt(9001))/(18),x=(1-sqrt(9001))/(18)

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x 0.9 (x + 1) = 25 + x

x = \frac{1 + 9001}{18}, x = \frac{1 - 9001}{18}

Decimal Notation

x = 5.32631 \dots, x = - 5.21520 \dots

Solution steps

x \cdot 0.9 (x + 1) = 25 + x

Multiply both sides by

10

9 x (x + 1) = 250 + 10 x

Expand

9 x (x + 1) : 9 x^{2} + 9 x

9 x^{2} + 9 x = 250 + 10 x

Move

10 x

to the left side

9 x^{2} - x = 250

Move

250

to the left side

9 x^{2} - x - 250 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 9 ( - 250 )}{2 \cdot 9}

(- 1)^{2} - 4 \cdot 9 (- 250) = 9001

x_{1, 2} = \frac{- ( - 1 ) \pm 9001}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 9001}{2 \cdot 9}, x_{2} = \frac{- ( - 1 ) - 9001}{2 \cdot 9}

x = \frac{- ( - 1 ) + 9001}{2 \cdot 9} : \frac{1 + 9001}{18}

x = \frac{- ( - 1 ) - 9001}{2 \cdot 9} : \frac{1 - 9001}{18}

The solutions to the quadratic equation are:

x = \frac{1 + 9001}{18}, x = \frac{1 - 9001}{18}

16 x^{2} + 40 x + 27 = 0

x^{2} - 10 x = 15

a, (a + 35)^{2} + a - b 5 = 51

x^{2} + 4 = 2 x

6 x^{2} + x + 2 = 0

What are the solutions to the equation x0.9(x+1)=25+x ?
The solutions to the equation x0.9(x+1)=25+x are x=(1+sqrt(9001))/(18),x=(1-sqrt(9001))/(18)
Find the zeros of x0.9(x+1)=25+x
The zeros of x0.9(x+1)=25+x are x=(1+sqrt(9001))/(18),x=(1-sqrt(9001))/(18)