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3 years ago

Solve the Quadratic Equation By Completing the Square b^2-15b-54=0

1 answer:

vladimir1956 [14]3 years ago

3 0

$b^{2}-15b-54=0. \newline
b^{2}-15b=54. \newline
b^{2}-15b+(\frac{15}{2})^{2}=54+(\frac{15}{2})^{2}. \newline
(b-\frac{15}{2})^{2}=\frac{441}{4}. \newline
b-\frac{15}{2}=\pm\frac{21}{2}. \newline
b=\pm\frac{21}{2}+\frac{15}{2}. \newline
b_1 = -3, b_2 = 18.$

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Collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and

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Answer:

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Step-by-step explanation:

collen family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Collen father would paint be a while that of her mother be b. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father a = 2b

Let the number of windows that would be needed to be painted each by Colleen and her 2 brothers be c because they would paint the equal number of windows.

The total number of windows to be painted = 2b + b + c + c + c = 3b + 3c = 3(b + c).

Collen painted 7 windows as her mother and her own share which is one less than the fathers share. Therefore b + c = 7.

Also the fathers share a = 2b = 7 + 1 = 8 windows. Therefore b = 4 which is the mother share

Therefore the total number of windows = 3(b + c) = 3(7) = 21 windows

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3(4) + 3c = 21

12 + 3c = 21

3c = 21 - 12

3c = 9

c = 3 which is collen and her brothers share

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