What are the solutions to the equation 1000(10+x)=100x^2 ?

The solutions to the equation 1000(10+x)=100x^2 are x=5(1+sqrt(5)),x=5(1-sqrt(5))

Find the zeros of 1000(10+x)=100x^2

The zeros of 1000(10+x)=100x^2 are x=5(1+sqrt(5)),x=5(1-sqrt(5))

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1000 (10 + x) = 100 x^{2}

x = 5 (1 + 5), x = 5 (1 - 5)

Decimal Notation

x = 16.18033 \dots, x = - 6.18033 \dots

Solution steps

1000 (10 + x) = 100 x^{2}

Expand

1000 (10 + x) : 10000 + 1000 x

10000 + 1000 x = 100 x^{2}

Switch sides

100 x^{2} = 10000 + 1000 x

Move

1000 x

to the left side

100 x^{2} - 1000 x = 10000

Move

10000

to the left side

100 x^{2} - 1000 x - 10000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1000 ) \pm ( - 1000 ) ^{2} - 4 \cdot 100 ( - 10000 )}{2 \cdot 100}

(- 1000)^{2} - 4 \cdot 100 (- 10000) = 10005

x_{1, 2} = \frac{- ( - 1000 ) \pm 1000 5}{2 \cdot 100}

Separate the solutions

x_{1} = \frac{- ( - 1000 ) + 1000 5}{2 \cdot 100}, x_{2} = \frac{- ( - 1000 ) - 1000 5}{2 \cdot 100}

x = \frac{- ( - 1000 ) + 1000 5}{2 \cdot 100} : 5 (1 + 5)

x = \frac{- ( - 1000 ) - 1000 5}{2 \cdot 100} : 5 (1 - 5)

The solutions to the quadratic equation are:

x = 5 (1 + 5), x = 5 (1 - 5)

(\frac{1}{4})^{\frac{1}{4}}

(1 + \frac{0.04}{4})^{4} - 1

- 138 > - 6 (6 b - 7)

x^{2} - 5 x = 8

0. 6^{2} + 0. 8^{2}

What are the solutions to the equation 1000(10+x)=100x^2 ?
The solutions to the equation 1000(10+x)=100x^2 are x=5(1+sqrt(5)),x=5(1-sqrt(5))
Find the zeros of 1000(10+x)=100x^2
The zeros of 1000(10+x)=100x^2 are x=5(1+sqrt(5)),x=5(1-sqrt(5))