Identify the steps in which the error occurred. There could be more than one answer

Question

x²+3x-18=-x²+2x-6

3x-18=2x-6 Step 1

5x=-24 Step 2

x= -24/5 Step 3

Answer 1

Hi Ighodalo A.

The curves intersect at

(2.212, -6.469) and (-2.712, _18.781)

If you try to set these up as two systems of equations they would appear to behave as below but they do not

Step 1 assumes that the x² terms cancel out not true, they add

Step 2 assumes that step 1 is true, step 1 is not true

3x - 18 = 2x - 6

3x - 2x = 18 - 6

x = 12

Plugging 12 into the original equations does not yield an equality

Step 3 solves for x incorrectly based on the steps 1 and 2. Step 3 does not move the variables across the equal sign correctly

x = -24/5 does not yield and equality when plugged into the orignal equations

Given

x²+3x-18=-x²+2x-6

I would start by moving everything over to one side of the equal sign

Step 1

x² + x² + 3x - 2x - 18 + 6 = 0

2x² + x - 12 = 0

Step 2

Apply the Quadratic Formula to the Quadratic Equation

a = 2

b = 1

c = -12

x = (-b±√(b²-4ac))/2a

The discriminant

√1-4(-12)(2)

√1+96

±√97

You have two positive roots

(√97 -1)/4

(-√97 - 1)/4

You can check my math in both your equations, you can also graph them at Desmos.com,

x = 2.2122 and x = -2.7122

You can try any of the solutions in your original equations, including x = -24/5 and x = 12

I hope you find this useful in identifying where these two parabolas intersect.

Answer 2

So, we always do the opposite operation and do the same thing to both sides.

x²+3x-18=-x²+2x-6

We can either subtract or add x² to both sides. We can't add the two sides together so x² and -x² cancel out. We end up with either...

2x² + 3x - 18 = 2x - 6 or 3x - 18 = -2x² + 2x - 6

Goingfrom the given Step 1 to Step 2, we'd subtract 2x and add 18 to both sides...

x = 12

We then wouldn't need Step 3, but it's correct as given.

Step 1 and Step 2 have errors.