To solve this equation, we can combine the two terms on the left side:

2^x + 2^x = 144

Since the bases are the same, we can add the exponents:

2 * 2^x = 144

Now, we can divide both sides by 2:

2^x = 144 / 2

2^x = 72

To solve for x, we can take the logarithm of both sides. Let's use the natural logarithm (ln):

ln(2^x) = ln(72)

Using the logarithmic property, we can bring down the exponent:

x * ln(2) = ln(72)

Now, divide both sides by ln(2):

x = ln(72) / ln(2)

Using a calculator, we can find the approximate value of x:

x ≈ 6.16993

Therefore, the solution to the equation 2^x + 2^x = 144 is x ≈ 6.16993.