What are the solutions to the equation completesquare (300+10x)(1.6-0.01x) ?

The solutions to the equation completesquare (300+10x)(1.6-0.01x) are -0.1(x-65)^2+902.5

Find the zeros of completesquare (300+10x)(1.6-0.01x)

The zeros of completesquare (300+10x)(1.6-0.01x) are -0.1(x-65)^2+902.5

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complete the square

(300 + 10 x) (1.6 - 0.01 x)

- 0.1 (x - 65)^{2} + 902.5

Solution steps

(300 + 10 x) (1.6 - 0.01 x)

Write in the standard form

a x^{2} + b x + c

- 0.1 x^{2} + 13 x + 480

Write

- 0.1 x^{2} + 13 x + 480

in the form:

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

Factor out

- 0.1

- 0.1 (x^{2} - \frac{13 x}{0.1} - \frac{480}{0.1})

2 a = - \frac{13}{0.1} : a = - 65

Add and subtract

(- 65)^{2}

- 0.1 (x^{2} - \frac{13 x}{0.1} - \frac{480}{0.1} + (- 65)^{2} - (- 65)^{2})

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

x^{2} - \frac{13}{0.1} x + (- 65)^{2} = (x - 65)^{2}

- 0.1 ((x - 65)^{2} - \frac{480}{0.1} - (- 65)^{2})

Simplify

- 0.1 (x - 65)^{2} + 902.5

5 x^{2} - 8 x + 16 = 0

\frac{1}{5} k (k + 4) = 0.5

w^{2} + 4 w = 0

x^{2} - 2 = 8

x^{2} + x - 56 = 0

What are the solutions to the equation completesquare (300+10x)(1.6-0.01x) ?
The solutions to the equation completesquare (300+10x)(1.6-0.01x) are -0.1(x-65)^2+902.5
Find the zeros of completesquare (300+10x)(1.6-0.01x)
The zeros of completesquare (300+10x)(1.6-0.01x) are -0.1(x-65)^2+902.5