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AlekseyPX
3 years ago
7

Which of the following statements describes one part of completing the square for x2 + 4x = 32?

Mathematics
1 answer:
SVEN [57.7K]3 years ago
7 0

Answer:

Step-by-step explanation:

I believe it is the 2nd one its the most logical

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Can someone help me with one pleaseT (ToT)
uysha [10]

Answer:

Add 1 to both sides.

Multiply both sides by -2.

Add 8 to both sides.

Divide both sides by 5.

Step-by-step explanation:

<u>Step 1</u>

-\dfrac{1}{2}(5x-8)-1=6\quad \quad \textsf{Write the equation.}

<u>Step 2</u>

-\dfrac{1}{2}(5x-8)=7 \quad \quad \textsf{Add 1 to both sides.}

This is called the <u>Addition Property of Equality</u>.  When the same number is added to both sides of an equation, the two sides remain equal.

\implies -\dfrac{1}{2}(5x-8)-1+1=6+1

\implies -\dfrac{1}{2}(5x-8)=7

<u>Step 3</u>

5x-8=-14 \quad \quad \textsf{Multiply both sides by -2.}

This is called the <u>Multiplication Property of Equality</u>.  When both sides of an equation are multiplied by the same number, the two sides remain equal.

\implies -2 \cdot -\dfrac{1}{2}(5x-8)=-2 \cdot 7

\implies 5x-8=-14

<u>Step 4</u>

5x=-6 \quad \quad \textsf{Add 8 to both sides.}

This is called the <u>Addition Property of Equality</u>.  When the same number is added to both sides of an equation, the two sides remain equal.

\implies 5x-8+8=-14+8

\implies 5x=-6

<u>Step 5</u>

x=-\dfrac{6}{5} \quad \quad \textsf{Divide both sides by 5.}

This is called the <u>Division Property of Equality</u>.  When both sides of an equation are divided by the same number, the two sides remain equal.

\implies \dfrac{5x}{5}=\dfrac{-6}{5}

\implies x=\dfrac{-6}{5}

<u>Conclusion</u>

<u></u>

<u />\begin{aligned}-\dfrac{1}{2}(5x-8)-1 & =6 & \quad \quad& \textsf{Write the equation.}\\\\-\dfrac{1}{2}(5x-8) & =7 & & \boxed{\textsf{Add 1 to both sides.}}\\\\5x-8 & =-14 & & \boxed{\textsf{Multiply both sides by -2.}}\\\\5x & =-6 & & \boxed{\textsf{Add 8 to both sides.}}\\\\x & =-\dfrac{6}{5} & & \boxed{\textsf{Divide both sides by 5.}}\\\end{aligned}

Learn more about Property Laws here:

brainly.com/question/28255621

brainly.com/question/28210762

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