Solve the following quadratic equation for all values of xx in simplest form.3, left bracket, x, minus, 4, right bracket, squared, equals, 273(x−4) 2 =27

Question

Solve the following quadratic equation for all values of xx in simplest form.

$3 \left( x - 4 \right)^2 = 273$

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Solution

Sure, let's solve the quadratic equation step by step:

Given equation is 3(x - 4)² = 27

Step 1: Divide both sides by 3 to simplify the equation:

(x - 4)² = 27/3

(x - 4)² = 9

Step 2: Take the square root of both sides:

x - 4 = ± √9

x - 4 = ± 3

Step 3: Solve for x:

x = 4 + 3 = 7 (for the positive root)

x = 4 - 3 = 1 (for the negative root)

So, the solutions to the equation are x = 7 and x = 1.

This problem has been solved

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