Sure, let's solve the equation step by step.
The given equation is:
[tex]\[ 3x^2 - 147 = 0 \][/tex]
### Step 1: Isolate the quadratic term
First, let's get the quadratic term by itself. We can do this by adding 147 to both sides of the equation:
[tex]\[ 3x^2 - 147 + 147 = 0 + 147 \][/tex]
[tex]\[ 3x^2 = 147 \][/tex]
### Step 2: Solve for [tex]\( x^2 \)[/tex]
Next, we need to isolate [tex]\( x^2 \)[/tex]. To do this, we divide both sides of the equation by 3:
[tex]\[ \frac{3x^2}{3} = \frac{147}{3} \][/tex]
[tex]\[ x^2 = 49 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, to find the value of [tex]\( x \)[/tex], we take the square root of both sides. Remember that taking the square root of a number results in both a positive and a negative solution:
[tex]\[ x = \pm \sqrt{49} \][/tex]
[tex]\[ x = \pm 7 \][/tex]
### Conclusion
So, the solutions to the equation [tex]\( 3x^2 - 147 = 0 \)[/tex] are:
[tex]\[ x = 7 \][/tex]
[tex]\[ x = -7 \][/tex]
These solutions can be written as:
[tex]\[ x = -7 \text{ and } x = 7 \][/tex]
Hence, the values of [tex]\( x \)[/tex] that satisfy the equation are [tex]\( -7 \)[/tex] and [tex]\( 7 \)[/tex].
