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

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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).