Math Help

Solving Quadratic Equations (continued…)

Step 2: Equate your two simultaneous equations.

Since both equations are equal to y, we just cut off the middle man (y) and equate the two equations. The left hand side is one equation and the right hand side is the other as shown below. It does not matter which side is which.

2x ² + 6x – 6 = 14x – 12

Step 3: Grouping terms to the left hand side.

Next, you want to group all the x ² terms together, the x terms together, and the number terms together. In the above equation, there is only one x ² term so no grouping is needed. There are, however, two terms involving x (6x and 14x). We want to group them all onto the left hand side of the equation so we bring 14x from the tight hand side to the left hand side. And, we do the same thing with 12.

This is as shown:

2x ² + 6x – 6 = 14x – 12

2x ² + 6x – 6 – 14x + 12 = 0

2x ² – 8x + 6 = 0

Step 4: Solve the quadratic equation.

Since the above quadratic equation (and all quadratic equations) are of the form ax ² + bx + c = 0, we can use the Quadratic Formula. Note that if you can see an easier way to spot the quadratic solutions, then there is no need to use the quadratic formula. The quadratic formula is only the back up when you cannot easily spot the quadratic roots by other methods.

In this case a = 2, b = -8, and c = 6

The root of x is then 3 or 1.

Since y = 14x – 12, y = 30 or 2.

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