What are the solutions to the equation completesquare-0.002x^2+0.4x+1.8 ?

The solutions to the equation completesquare-0.002x^2+0.4x+1.8 are -0.002(x-100)^2+21.8

Find the zeros of completesquare-0.002x^2+0.4x+1.8

The zeros of completesquare-0.002x^2+0.4x+1.8 are -0.002(x-100)^2+21.8

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complete the square

- 0.002 x^{2} + 0.4 x + 1.8

- 0.002 (x - 100)^{2} + 21.8

Solution steps

- 0.002 x^{2} + 0.4 x + 1.8

Write

- 0.002 x^{2} + 0.4 x + 1.8

in the form:

x^{2} + 2 a x + a^{2}

Factor out

- 0.002

- 0.002 (x^{2} - \frac{0.4 x}{0.002} - \frac{1.8}{0.002})

2 a = - \frac{0.4}{0.002} : a = - 100

Add and subtract

(- 100)^{2}

- 0.002 (x^{2} - \frac{0.4 x}{0.002} - \frac{1.8}{0.002} + (- 100)^{2} - (- 100)^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} - \frac{0.4}{0.002} x + (- 100)^{2} = (x - 100)^{2}

- 0.002 ((x - 100)^{2} - \frac{1.8}{0.002} - (- 100)^{2})

Simplify

- 0.002 (x - 100)^{2} + 21.8

(2 x - 1) (2 x - 5) = 32

3 x^{2} + 18 = 5 x^{2}

24 x^{2} + 162 x - 42 = 0

x^{2} = 17 x - 72

(2 x + 3) (x - 1) = 42

What are the solutions to the equation completesquare-0.002x^2+0.4x+1.8 ?
The solutions to the equation completesquare-0.002x^2+0.4x+1.8 are -0.002(x-100)^2+21.8
Find the zeros of completesquare-0.002x^2+0.4x+1.8
The zeros of completesquare-0.002x^2+0.4x+1.8 are -0.002(x-100)^2+21.8