What are the solutions to the equation x=0.25x^2-14.5x+200 ?

The solutions to the equation x=0.25x^2-14.5x+200 are x=31+sqrt(161),x=31-sqrt(161)

Find the zeros of x=0.25x^2-14.5x+200

The zeros of x=0.25x^2-14.5x+200 are x=31+sqrt(161),x=31-sqrt(161)

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x = 0.25 x^{2} - 14.5 x + 200

x = 31 + 161, x = 31 - 161

Decimal Notation

x = 43.68857 \dots, x = 18.31142 \dots

Solution steps

x = 0.25 x^{2} - 14.5 x + 200

Multiply both sides by

100

x \cdot 100 = 25 x^{2} - 1450 x + 20000

Switch sides

25 x^{2} - 1450 x + 20000 = x \cdot 100

Move

x 100

to the left side

25 x^{2} - 1550 x + 20000 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1550 ) \pm ( - 1550 ) ^{2} - 4 \cdot 25 \cdot 20000}{2 \cdot 25}

(- 1550)^{2} - 4 \cdot 25 \cdot 20000 = 50161

x_{1, 2} = \frac{- ( - 1550 ) \pm 50 161}{2 \cdot 25}

Separate the solutions

x_{1} = \frac{- ( - 1550 ) + 50 161}{2 \cdot 25}, x_{2} = \frac{- ( - 1550 ) - 50 161}{2 \cdot 25}

x = \frac{- ( - 1550 ) + 50 161}{2 \cdot 25} : 31 + 161

x = \frac{- ( - 1550 ) - 50 161}{2 \cdot 25} : 31 - 161

The solutions to the quadratic equation are:

x = 31 + 161, x = 31 - 161

y, x = y^{2} - 8 y + 3

0.05 x^{2} - 0.08 x = 0

- 2 x^{2} + 100 x

x^{2} - 40 x + 1200 = 0

(2 x + 4) (x - 7) = 2 (5 x - 3)

What are the solutions to the equation x=0.25x^2-14.5x+200 ?
The solutions to the equation x=0.25x^2-14.5x+200 are x=31+sqrt(161),x=31-sqrt(161)
Find the zeros of x=0.25x^2-14.5x+200
The zeros of x=0.25x^2-14.5x+200 are x=31+sqrt(161),x=31-sqrt(161)