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Yakvenalex [24]
3 years ago
6

Solve by transforming into a perfect square trinomial x squared-14x=15

Mathematics
1 answer:
ycow [4]3 years ago
8 0
X^2 - 14 x  = 15

(x - 7)^2 - 49 = 15

(x-7)^2 = 64

x - 7 = - or  + 8

x = 15  or -1 

Just take half o the coefficient of x and subtract it squared as above.

In general

x^2 + ax = b

(x + a/2)^2 - a^2/4 = b 

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Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step

That is (\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4} Calvin's step is the correct step.Because this is the correct way to do simplify the rational expression. And also because Nadine made a blender mistake in her operations in step

Step-by-step explanation:

Given that Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4

Their expression can be written as below

(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}

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That is \frac{r^{20}s^{12}}{r^{-32}s^8}

Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4

That is r^{-13}s^{-1}

Now simplify the given expression to check whose step is correct:

(\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}

=(r^{-5}s^{-3}r^{-8}s^{2})^{-4} ( using the property \frac{1}{a^m}=a^{-m} )

=(r^{-5-8}s^{-3+2})^{-4}

=(r^{-13}s^{-1})^{-4}

Therefore (\frac{r^{-5}s^{-3}}{r^8s^{-2}})^{-4}=(r^{-13}s^{-1})^{-4}

Therefore Calvin's first step is to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4 is the correct step.

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