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mojhsa [17]
3 years ago
6

Find the solution to the following equation by transforming it into a perfect square trinomial.

Mathematics
2 answers:
Alja [10]3 years ago
6 0
x^{2} -12x=13\ \ \ \Leftrightarrow\ \ \ x^2-2\cdot x\cdot 6+6^2-6^2=13\\\\ \Leftrightarrow\ \ \ (x-6)^2=13+36\ \ \ \Leftrightarrow\ \ \ (x-6)^2=49\ \ \ \Leftrightarrow\ \ \ (x-6)^2=7^2\\\\x-6=7\ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ x-6=-7\\\\x=13\ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ x=-1\\\\Ans.\ x\in \{-1,\ 13\}
alexandr1967 [171]3 years ago
4 0
X² -12x  = 13                       way to obtain 36   >       (-12/2)²  =  36    
x²  -12x + 36 =13 +36      since we add 36 to the left,we must also add 36 to the right
(x-6)²  =  49
x-6  =    7
x  =    7 + 6 =  13    or      -7 + 6  = -1
x =  -1    or    13
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Find the slope in (-2,8) and (1,6)
Salsk061 [2.6K]

Formula for slope: \frac{y2 - y1}{x2 - x1}

y₂: 6

y₁: 8

x₂: 1

x₁: -2

Plug them into the slope equation:

\frac{6 - 8}{1 - (-2)}

--> \frac{-2}{1 + 2}

---> -\frac{2}{3}

The slope is -\frac{2}{3}.

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prisoha [69]
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3 years ago
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ra1l [238]
<h3>Answer:   5</h3>

=================================================

Work Shown:

x^2 - 5x + 1 = 0

x^2 + 1 - 5x = 0

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---------------

An alternative method involves solving the original equation using the quadratic formula. After you get the two roots x = p and x = q, you should be able to find that p + 1/p = 5 and also q + 1/q = 5 as well.

In this case,

p = (5 + sqrt(21))/2

q = (5 - sqrt(21))/2

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3 years ago
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As we know that 8/25 is greater than 1/5

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