Using completing the square solve for x X^2-10x-9=0

1 answer:

7 0

X^2 - 10x - 9 = 0
first we will move the constant term to the other side
x^2 - 10x = 9
then, to both sides we will add the number that makes the polynomial on the left a perfect square trinomial. Take half of the coefficient of x, then square it. half of the coefficient of x (-10) is -5, and -5 squared is 25. so:
x^2 - 10x + 25 = 34
factor the perfect square trinomial
(x - 5)^2 = 34
x - 5 = plus or minus sqrt(34)
x = 5 plus or minus sqrt(34)

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A rectangle has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the l

Lorico [155]

❍ Concept :-

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We have been provided with some information regarding a rectangular shaped mat. And on the basis of that information, we will create some assumptions and create and equation and equate it to get our required answer.

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✱ Given Information :-

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A rectangular mat with,

Perimeter = 36 ft.
Length = twice the width

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✱ To Find :-

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The dimensions of the mat
Area of the mat

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✱ Formula Used :-

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$\diamond \: \underline{ \boxed{\begin{array}{cc} \sf1. \: Perimeter_{Rectangle} = 2(l+b) \\ \\ \sf 2. ~Area_{Rectangle} = l\times b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}}} \: \star \\$

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✱ Solution :-

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Let the breadth of the mat be x, therefore,

Length = 2x

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Now, according to the question,

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$\sf \hookrightarrow 36 \: = 2(2x + x) \\ \\ \\ \sf \hookrightarrow 6x = 36 \: ft. \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow x = \cancel\frac{36}{6} = 6 \: ft. \: \: \\$