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3 years ago

8

X^2+4x=-3what would be the steps to find the answer of this equation?to find x

1 answer:

Verizon [17]3 years ago

7 0

X^2+4x=-3
x^2+4x+3=0
(x+1)(x+3)=0
x+1=0 so x=-1
x+3=0 so x=-3
so the solution is x=-3,-1
Hope this helped! Please rate my answer if I helped you! Any questions please feel free to ask! Thank you so much!

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Radius: $r =\frac{\sqrt {21}}{6}$

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Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

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Where

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So, we have:

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Group the expression into 2

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$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

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Add the fractions

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$r =\frac{\sqrt {84}}{12}$

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$r =\frac{2\sqrt {21}}{12}$

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Where

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$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

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