Reconciliations of the changes in the carrying value of goodwill for the first nine months of 2020 and for the year ended December 31, 2019 follow (in millions).

	September 30, 2020			December 31, 2019
Balance at beginning of year	$	81,882		$	81,025
Acquisitions of businesses		25			890
Impairment charges		(10,021	)		—
Other, including foreign currency translation		(21	)		(33	)
Balance at end of period	$	71,865		$	81,882

Other intangible assets and related accumulated amortization are summarized as follows (in millions).

	September 30, 2020				December 31, 2019
	Gross carrying amount		Accumulated amortization		Gross carrying amount		Accumulated amortization
Insurance and other:
Customer relationships	$	27,344	$	5,548	$	27,943	$	5,025
Trademarks and trade names		5,193		774		5,286		759
Patents and technology		4,720		3,255		4,560		3,032
Other		3,319		1,347		3,364		1,286
	$	40,576	$	10,924	$	41,153	$	10,102
Railroad, utilities and energy:
Customer relationships	$	678	$	352	$	678	$	324
Trademarks, trade names and other		325		91		325		84
	$	1,003	$	443	$	1,003	$	408

Intangible asset amortization expense in the first nine months was $962 million in 2020 and $986 million in 2019. Intangible assets with indefinite lives were $18.3 billion as of September 30, 2020 and $19.0 billion as of December 31, 2019 and primarily related to certain customer relationships and trademarks and trade names.

During the second quarter of 2020, we concluded it was necessary to reevaluate goodwill and indefinite-lived intangible assets of certain of our reporting units for impairment due to the disruptions arising from the COVID-19 pandemic. We believed that the most significant of these disruptions related to the air travel and commercial aerospace and supporting industries. We recorded pre-tax goodwill impairment charges of approximately $10 billion and pre-tax indefinite-lived intangible asset impairment charges of $638 million in the second quarter of 2020. Approximately $10 billion of these charges related to Precision Castparts Corp. (“PCC”), the largest business within Berkshire's manufacturing segment. The carrying value of PCC-related goodwill and indefinite-lived intangible assets prior to the impairment charges was approximately $31 billion.

The amounts of the impairment charges were determined based on discounted cash flow methods and reflect our current assessments of the risks and uncertainties associated with the aerospace industry. Significant judgment is required in estimating the fair value of a reporting unit and in performing impairment tests. Due to the inherent uncertainty in forecasting cash flows and earnings, actual results in the future may vary significantly from the forecasts.

Disruptions arising from the COVID-19 pandemic will likely continue to evolve and the effects on our businesses may differ from what we currently estimate. If the effects prove to be worse than is reflected in our current estimates, additional goodwill or indefinite-lived intangible asset impairment charges could be required.