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Solve for x, rounded off to TWO decimal places where necessary: x(3-x) = -3

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christiano-cr7 | Salutatorian

Posted July 24, 2013 at 7:59 AM via web

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Solve for x, rounded off to TWO decimal places where necessary:

x(3-x) = -3

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted July 24, 2013 at 8:52 AM (Answer #1)

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`` Prep the equation.
*  Any variable without a coefficient automatically gets a 1.
*  Change subtraction signs into addition of the opposite

Change 3 - x into 3 - 1x
Change 3 - 1x into 3 + (-1x)

So now the prepped equation is...
x * (3 + (-1x)) = -3

Use the Distributive Property.
x * (3 + (-1x)) = -3
3x + (-1x^2) = -3

Rewrite the equation in standard form.
Standard form is:  ax^2 + bx + c = 0
3x + (-1x^2) = -3
-1x^2 + 3x = -3
-1x^2 + 3x + 3 = -3 + 3
-1x^2 + 3x + 3 = 0

Identity the values of a, b, and c.
-1x^2 + 3x + 3 = 0
a = -1
b = 3
c = 3

Now use the Quadratic Formula to solve for x.


          -b ± sqrt(b^2 - 4ac)
x =     ------------------------
                      2a

 

Substitute -1, 3, and 3 in for a, b, and c respectively.

 

          -3 ± sqrt(3^2 - 4 * -1 * 3)
x =     -------------------------------                       
                         2 * -1

 

Now follow order of operations to simplify.

 

          -3 ± sqrt(9 - 4 * -1 * 3)
x =     ----------------------------- 
                        2 * -1

 

           -3 ± sqrt(9 - (-12))
x =     -------------------------
                       -2

 

           -3 ± sqrt(21)
x =     ----------------- 
                    -2

 

21 is not a perfect square, so we shall round off to two decimal places from now on.

 

           -3 ± 4.58
x =      ----------- 
                 -2

 

Now is where the problem splits in two, one for + and one for -.
First using addition:

 

           -3 + 4.58               1.58                    
x =      -----------     =     ---------     =     -0.79
                 -2                     -2

 

Next using subtraction:

 

           -3 - 4.58                -7.58                   
x =      -----------     =     ---------     =     3.79                 
                -2                      -2

 

The solution set for x is {-0.79, 3.79}

 

These solutions can be found as x-intercepts of the graph of the parabola.

 

Notice that the parabola intercepts the x-axis at (-0.79, 0) and (3.79, 0).

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