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Solve the following quadratic equation:

[tex]\[(x-16)^2 = 256\][/tex]

A. [tex]\(x = -32\)[/tex] and [tex]\(x = 0\)[/tex]

B. [tex]\(x = 30\)[/tex] and [tex]\(x = -4\)[/tex]

C. [tex]\(x = -30\)[/tex] and [tex]\(x = 4\)[/tex]

D. [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex]

Sagot :

GinnyAnswer
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]
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