Let's solve the equation step by step:
The given equation is:
[tex]\[ 16x^2 + 9 = 25 \][/tex]
First, we move the constant term on the right side to the left side by subtracting 25 from both sides of the equation:
[tex]\[ 16x^2 + 9 - 25 = 0 \][/tex]
[tex]\[ 16x^2 - 16 = 0 \][/tex]
Next, simplify the equation:
[tex]\[ 16x^2 - 16 = 0 \][/tex]
Factor out the common factor on the left-hand side:
[tex]\[ 16(x^2 - 1) = 0 \][/tex]
Now, set each factor equal to zero:
[tex]\[ x^2 - 1 = 0 \][/tex]
To solve for [tex]\( x \)[/tex], we move the constant term to the right side:
[tex]\[ x^2 = 1 \][/tex]
Taking the square root of both sides gives:
[tex]\[ x = \pm 1 \][/tex]
This means the solutions to the equation are:
[tex]\[ x = -1 \][/tex]
and
[tex]\[ x = 1 \][/tex]
Based on these solutions, the correct answer is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = 1 \)[/tex]
