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Is the equation 3 + x = 24 / ( x + 1 )  a quadratic?

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fairydrink | Student, Grade 10 | eNoter

Posted June 1, 2011 at 2:24 AM via web

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Is the equation 3 + x = 24 / ( x + 1 )  a quadratic?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted March 20, 2013 at 6:25 PM (Answer #3)

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You need to perform cross multiplication, such that:

`(3 + x)(x + 1) = 24 => 3(x + 1) + x(x + 1) = 24`

`3x + 3 + x^2 + x = 24 => x^2 + 4x + 3 - 24 = 0`

`x^2 + 4x - 21 = 0`

You may evaluate the solutions to quadratic equation, using quadratic formula, such that:

`x_(1,2) = (-4+-sqrt(16 + 84))/2 => x_(1,2) = (-4+-sqrt100)/2`

`x_(1,2) = (-4+-10)/2 => x_1 = 3 ; x_2 = -7`

Hence, evaluating the solutions to the given quadratic equation, yields `x_1 = 3 ; x_2 = -7.`

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giorgiana1976 | College Teacher | Valedictorian

Posted June 2, 2011 at 1:10 AM (Answer #2)

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We'll have to multiply both sides by x+1:

3(x+1) + x(x+1) = 24

We'll remove the brackets:

3x + 3 + x^2 + x - 24 = 0

We'll combine like terms:

x^2 + 4x - 21 = 0

Since the order of the equation is two, therefore, the equation is a quadratic.

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