Question

solve by completing the square. type the answers from smallest to largest.\\(x^2 + 26x + 48 = 0\\)\\(x = \square\\) or \\(x = \square\\)\
type the smaller solution here! \
type the larger solution here!

Explanation:

Step1: Isolate the x-terms

Subtract 48 from both sides: \( x^2 + 26x = -48 \)

Step2: Complete the square

Take half of 26, which is 13, square it: \( 13^2 = 169 \). Add to both sides:
\( x^2 + 26x + 169 = -48 + 169 \)
Simplify: \( (x + 13)^2 = 121 \)

Step3: Solve for x

Take square roots: \( x + 13 = \pm\sqrt{121} = \pm11 \)
Subtract 13: \( x = -13 \pm 11 \)
So, \( x = -13 + 11 = -2 \) or \( x = -13 - 11 = -24 \)

Answer:

\( x = -24 \) or \( x = -2 \) (smaller: \(-24\), larger: \(-2\))