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Lostsunrise [7]
3 years ago
8

What number must you add to complete the square? x^2 + 2x = -1

Mathematics
2 answers:
Andru [333]3 years ago
6 0
\large\begin{array}{l} \textsf{You must add 1 to complete the square.}\\\\ \textsf{There is a very common special product: (square of a sum)}\\\\ \mathsf{(a+b)^2=a^2+2ab+b^2}\\\\\\ \textsf{Take the given equation:}\\\\ \mathsf{x^2+2x=-1\qquad(i)}\\\\\\ \textsf{The first term is a square (x squared)}\\\\ \textsf{The second term is a product of 2, x and 1.} \end{array}


\large\begin{array}{l}\\\\\\ \textsf{We need to find a proper value for b, so that if we add it to}\\\textsf{the left side of the equation, we get a perfect square.}\\\\ \textsf{So,}\\\\ \begin{array}{cccccccccc} \mathsf{a^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{a}&\!\!\!\cdot\!\!\!&\mathsf{b}&\!\!\!+\!\!\!&\mathsf{b^2}&=\mathsf{(a+b)^2}\\\\ \mathsf{\downarrow}&&&\!\!\!\!\!&\downarrow&\!\!\!\!\!&\downarrow&&\downarrow\\\\ \mathsf{x^2}&\!\!\!+\!\!\!&\mathsf{2}&\!\!\!\cdot\!\!\!&\mathsf{x}&\!\!\!\cdot\!\!\!&\mathsf{1}&\!\!\!+\!\!\!&\mathsf{1^2}&=\mathsf{(x+1)^2} \end{array}\\\\\\ \textsf{Just by comparing the expressions above, we can conclude that}\\\textsf{b must be equal to 1, so we get a perfect square:}\\\\ \mathsf{(x+1)^2=x^2+2x+1} \end{array}


\large\begin{array}{l}\\\\\\ \textsf{Back to (i), adding 1 to both sides:}\\\\ \mathsf{x^2+2x+1=-1+1}\\\\ \boxed{\begin{array}{c} \mathsf{(x+1)^2=0} \end{array}} \end{array}


\large\begin{array}{l}\\\\\\ \textsf{If you want to solve this equation for x, you will find}\\\\ \mathsf{x+1=0}\\\\ \mathsf{x=-1}\quad\longleftarrow\quad\textsf{(solution)} \end{array}


If you're having problems understanding the answer, try seeing it through your browser: brainly.com/question/2112248


\large\begin{array}{l} \textsf{Any doubt? Please, comment below.}\\\\\\ \textsf{Best regards! :-)} \end{array}

netineya [11]3 years ago
3 0
To begin completing the square, it must be equivalent to 0. 

x^2 + 2x + 1 = 0

Therefore, add 1. 
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7a^2b + 10a^2b^2 + 14a^2b^3 =
a^2b (7 + 10b + 14b^2) <==
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0.402,0.42,0375,12<br> Order from least yo greatest
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0.402, 0.42, 12, 375

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Erin has 5 cans of juice and drinks 13 of a can daily. In how many days will she empty all the cans she has?
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Answer:

15 days

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Don't you mean 1/3?  If so,

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3 years ago
2/3 + 1/2 in simple form fractions
nata0808 [166]
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3 0
3 years ago
The senior class want to play a practical joke on the principal, who was a former college basketball star. They want to fill his
steposvetlana [31]

The number of basketball that will fill up the entire office is <u>approximately 16,615.</u>

<em><u>Recall:</u></em>

Volume of a spherical shape = \frac{4}{3} \pi r^3

Volume of a rectangular prism = l \times w \times h

<em><u>Given:</u></em>

Diameter of basketball = 9.5 in.

Radius of the ball = 1/2 of 9.5 = 4.75 in.

Radius of the ball in ft = 0.4 ft (12 inches = 1 ft)

Dimension of the office (rectangular prism) = 20 ft by 18 ft by 12 ft

  • First, find the volume of the basketball:

Volume of ball = \frac{4}{3} \pi r^3 = \frac{4}{3} \times \pi \times 4.75^3\\

Volume of basketball = 448.92 $ in^3

  • Convert to ft^3

1728 $ in.^3 = 1 $ ft^3

<em>Therefore,</em>

  • Volume of basketball = \frac{448.92}{1728} = 0.26 $ ft^3

  • Find the volume of the office (rectangular prism):

Volume of the office = 20 \times 18 \times 12 = 4,320 $ ft^3

  • Number of basket ball that will fill the office = Volume of office / volume of basketball

  • <em>Thus:</em>

Number of basket ball that will fill the office = \frac{4,320}{0.26} = 16,615

Therefore, it will take approximately <u>16,615 balls</u><u> to fill up the entire office</u>.

Learn more here:

brainly.com/question/16098833

6 0
2 years ago
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