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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.

Quadratic equations are not difficult to solve if you follow a process. Always use the same logic to solve quadratic equations. The method of solving quadratic equations below will show you how to solve quadratic equations every time. Whenever you are faced with solving quadratic equations, you can use the following method of solving quadratic equations. 

Quadratic equation and simultaneous equations you have to solve

Suppose you are trying to solve the following quadratic equation simultaneous equations: 

y = 2x ² + 6x – 6 

y + 12 = 14x 

Solution to the simultaneous equations involving quadratic equation

Step 1: Rearrange the simultaneous equations 

The first thing to do in solving simultaneous equations involving quadratic equations is to re-organize the equations so that we can compare apples to apples. In another word, re arrange the simultaneous equations so that y is on the left hand side for both equations on its own as shown below. 

• The first equation is y = 2x ² + 6x – 6. Since y is already on the right hand side on its own, there is nothing to be done for the first equation at this stage.

Now we have two simultaneous equations involving quadratic equation as follows: 

y = 2x ² + 6x – 6 

y = 14x � 12