Evaluate the expression:
$(-5)^2-2 \times(-9)+6$
The objective is to compute the value of the arithmetic expression \((-5)^2 - 2 \times (-9) + 6\). According to the order of operations (PEMDAS/BODMAS), we must address exponents first, then multiplication, and finally addition and subtraction from left to right.
First, we evaluate the exponent: \((-5)^2\). Since \((-5) \times (-5) = 25\), the expression simplifies to \(25 - 2 \times (-9) + 6\).
Next, we address the multiplication: \(2 \times (-9) = -18\). The expression now becomes \(25 - (-18) + 6\). Subtracting a negative number is equivalent to adding its positive counterpart, so \(25 - (-18) + 6 = 25 + 18 + 6\).
Finally, we perform the remaining addition: \(25 + 18 = 43\), and \(43 + 6 = 49\). The final result of the expression is \(\boxed{49}\).
Understanding the order of operations is essential for balancing a budget or managing simple logistics. For example, if you start with an initial investment of 25 dollars, then encounter a series of transactions like subtracting a debt of 18 dollars (which technically adds to your balance if the debt is cancelled) and adding a final payment of 6 dollars, you would calculate your total balance as \(25 - (-18) + 6 = 49\) dollars. This logical approach helps in accurately tracking finances and solving daily quantitative problems.