What are the solutions to the equation 1-0.5x+0.05x^2=0 ?

The solutions to the equation 1-0.5x+0.05x^2=0 are x=5+sqrt(5),x=5-sqrt(5)

Find the zeros of 1-0.5x+0.05x^2=0

The zeros of 1-0.5x+0.05x^2=0 are x=5+sqrt(5),x=5-sqrt(5)

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1 - 0.5 x + 0.05 x^{2} = 0

x = 5 + 5, x = 5 - 5

Decimal Notation

x = 7.23606 \dots, x = 2.76393 \dots

Solution steps

1 - 0.5 x + 0.05 x^{2} = 0

Multiply both sides by

100

100 - 50 x + 5 x^{2} = 0

Write in the standard form

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

5 x^{2} - 50 x + 100 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 50 ) \pm ( - 50 ) ^{2} - 4 \cdot 5 \cdot 100}{2 \cdot 5}

(- 50)^{2} - 4 \cdot 5 \cdot 100 = 105

x_{1, 2} = \frac{- ( - 50 ) \pm 10 5}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 50 ) + 10 5}{2 \cdot 5}, x_{2} = \frac{- ( - 50 ) - 10 5}{2 \cdot 5}

x = \frac{- ( - 50 ) + 10 5}{2 \cdot 5} : 5 + 5

x = \frac{- ( - 50 ) - 10 5}{2 \cdot 5} : 5 - 5

The solutions to the quadratic equation are:

x = 5 + 5, x = 5 - 5

x^{2} - x + 10 = 10 x

24 x^{2} - 24 = 0

x^{2} - 2 x + 1 = 2 - 4 x

(z + 3)^{2} = 0

x^{2} = \frac{8.9}{9.4} \cdot (x + 0.8)^{2}

What are the solutions to the equation 1-0.5x+0.05x^2=0 ?
The solutions to the equation 1-0.5x+0.05x^2=0 are x=5+sqrt(5),x=5-sqrt(5)
Find the zeros of 1-0.5x+0.05x^2=0
The zeros of 1-0.5x+0.05x^2=0 are x=5+sqrt(5),x=5-sqrt(5)