Solve the equation 2x-x(x+4)=(x+5)(x+2)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation to be solved is 2x-x(x+4)=(x+5)(x+2).

2x-x(x+4)=(x+5)(x+2)

=> 2x - x^2 - 4x = x^2 + 5x + 2x + 10

=> 2x^2 + 9x + 10 = 0

=> 2x^2 + 4x + 5x + 10 = 0

=> 2x(x + 2) + 5(x + 2) = 0

=> (2x + 5)(x + 2) = 0

=> x = -2.5 and x = -2

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najm1947 | Elementary School Teacher | (Level 1) Valedictorian

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Simplify the given equation 2x-x(x+4)=(x+5)(x+2) as under: 

2x-x(x+4)=(x+5)(x+2)

2x-x^2-4x=x^2+2x+5x-10

2x-X^2-4x-x^2-2x-5x-10 = 0

-2x^2-9x-10 = 0

2x^2+9x+10 = 0

This is in the form ax^2+bx+c = 0

where a=2, b=9 and c=10

using the formula we get two roots of x as:

x = (-b+sqrt(b^2-4ac))/(2a) and x=(-b+sqrt(b^2-4ac))/(2a)

x=(-9+sqrt((9^2)-4*2*10)/(2*2) = (-9+1)/(4) = -2 and

x=(-9-sqrt((9)^2-4*2*10)/(2*2) = (-9-1)/(4) = -2.5

The solution to the given equation is x = -2 and x = -2.5

 

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