What is the factor form of 2x^2-25=0 and -4x^2+81=0

1 answer:

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$2x^2-25=0\\\\(x\sqrt2)^2=5^2=0\\\\(x\sqrt2-5)(x\sqrt2+5)=0\\-------------------------\\-4x^2+81=0\\\\81-4x^2=0\\\\9^2-(2x)^2=0\\\\(9-2x)(9+2x)=0\\------------------------\\Used:\\(a-b)(a+b)=a^2-b^2$

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PROBLEM: Riley has a rectangular shaped patio that is 13 feet long by 15 feet wide. He wants to DOUBLE THE AREA of the patio by

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Answer:

1) The equation that represents the total area of Riley's proposed ratio is $A' = (\sqrt{2}\cdot x)\cdot (\sqrt{2}\cdot y)$ .

2) The length and width of the new patio are approximately 18.4 feet and 21.2 feet, respectively.

Step-by-step explanation:

1) From Geometry we remember that area formula for the rectangle is represented by:

$A = x\cdot y$ (1)

Where:

$A$ - Area, measured in square feet.

$x$ - Length, measured in feet.

$y$ - Width, measured in feet.

From statement we know that Riley wants to double the area, that is:

$A' = 2\cdot A$ (2)

By applying (1) in (2), we get the following expression:

$A' = 2\cdot x\cdot y$ (3)

Given that Riley wants to double the area of the pation by increasing the length and width by the same amount, we can rearrange (3) by algebraic means:

$A' = \sqrt{2}\cdot \sqrt{2}\cdot x\cdot y$