Certainly! Let's solve the equation step-by-step together:
The given equation is:
[tex]\[ 4x^2 + 72 = 6x^2 \][/tex]
Step 1: Move all terms to one side of the equation.
We need to move all the terms involving [tex]\(x\)[/tex] to one side of the equation and constants to the other side. In this case, we can subtract [tex]\(4x^2\)[/tex] from both sides:
[tex]\[ 4x^2 + 72 - 4x^2 = 6x^2 - 4x^2 \][/tex]
Simplifying this, we get:
[tex]\[ 72 = 2x^2 \][/tex]
Step 2: Isolate the term involving [tex]\(x^2\)[/tex].
Next, we divide both sides of the equation by 2 to isolate [tex]\(x^2\)[/tex]:
[tex]\[ \frac{72}{2} = x^2 \][/tex]
Simplifying this, we obtain:
[tex]\[ 36 = x^2 \][/tex]
Step 3: Solve for [tex]\(x\)[/tex].
Now, we need to find the value(s) of [tex]\(x\)[/tex] that satisfy [tex]\(x^2 = 36\)[/tex]. To do this, we take the square root of both sides:
[tex]\[ x = \pm\sqrt{36} \][/tex]
Evaluating the square root, we get:
[tex]\[ x = \pm 6 \][/tex]
Thus, the solutions to the equation [tex]\(4x^2 + 72 = 6x^2\)[/tex] are:
[tex]\[ x = 6 \text{ and } x = -6 \][/tex]
