Answer :
To solve the quadratic equation [tex]\((x - 16)^2 = 256\)[/tex], follow these steps:
1. Take the square root of both sides:
[tex]\[ \sqrt{(x - 16)^2} = \sqrt{256} \][/tex]
2. Simplify the equation:
[tex]\[ |x - 16| = 16 \][/tex]
3. Set up the two possible equations based on the absolute value:
[tex]\[ x - 16 = 16 \quad \text{or} \quad x - 16 = -16 \][/tex]
4. Solve each equation separately:
- For [tex]\(x - 16 = 16\)[/tex]:
[tex]\[ x - 16 = 16 \][/tex]
[tex]\[ x = 16 + 16 \][/tex]
[tex]\[ x = 32 \][/tex]
- For [tex]\(x - 16 = -16\)[/tex]:
[tex]\[ x - 16 = -16 \][/tex]
[tex]\[ x = 16 - 16 \][/tex]
[tex]\[ x = 0 \][/tex]
So, the solutions to the equation are [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex], which corresponds to:
D. [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex]
1. Take the square root of both sides:
[tex]\[ \sqrt{(x - 16)^2} = \sqrt{256} \][/tex]
2. Simplify the equation:
[tex]\[ |x - 16| = 16 \][/tex]
3. Set up the two possible equations based on the absolute value:
[tex]\[ x - 16 = 16 \quad \text{or} \quad x - 16 = -16 \][/tex]
4. Solve each equation separately:
- For [tex]\(x - 16 = 16\)[/tex]:
[tex]\[ x - 16 = 16 \][/tex]
[tex]\[ x = 16 + 16 \][/tex]
[tex]\[ x = 32 \][/tex]
- For [tex]\(x - 16 = -16\)[/tex]:
[tex]\[ x - 16 = -16 \][/tex]
[tex]\[ x = 16 - 16 \][/tex]
[tex]\[ x = 0 \][/tex]
So, the solutions to the equation are [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex], which corresponds to:
D. [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex]