What are the solutions to the equation completesquare-1/10 (x+10)(x-20) ?

The solutions to the equation completesquare-1/10 (x+10)(x-20) are -1/10 (x-5)^2+45/2

Find the zeros of completesquare-1/10 (x+10)(x-20)

The zeros of completesquare-1/10 (x+10)(x-20) are -1/10 (x-5)^2+45/2

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complete the square

- \frac{1}{10} (x + 10) (x - 20)

- \frac{1}{10} (x - 5)^{2} + \frac{45}{2}

Solution steps

- \frac{1}{10} (x + 10) (x - 20)

Write in the standard form

a x^{2} + b x + c

- \frac{x ^{2}}{10} + x + 20

Write

- \frac{x ^{2}}{10} + x + 20

in the form:

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

Factor out

- \frac{1}{10}

- \frac{1}{10} (x^{2} - 10 x - 200)

2 a = - 10 : a = - 5

Add and subtract

(- 5)^{2}

- \frac{1}{10} (x^{2} - 10 x - 200 + (- 5)^{2} - (- 5)^{2})

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

x^{2} - 10 x + (- 5)^{2} = (x - 5)^{2}

- \frac{1}{10} ((x - 5)^{2} - 200 - (- 5)^{2})

Simplify

- \frac{1}{10} (x - 5)^{2} + \frac{45}{2}

100 x - x^{2} + 800 = 0

7 x^{2} + 4 \cdot (- 3) = 0

(x - \frac{1}{2})^{2} = x - \frac{1}{2}

y, y^{2} - 8 y + 16 = 0

7 d^{2} + 8 d - 3 = 0

What are the solutions to the equation completesquare-1/10 (x+10)(x-20) ?
The solutions to the equation completesquare-1/10 (x+10)(x-20) are -1/10 (x-5)^2+45/2
Find the zeros of completesquare-1/10 (x+10)(x-20)
The zeros of completesquare-1/10 (x+10)(x-20) are -1/10 (x-5)^2+45/2