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 bracket, x, minus, 4, right bracket, squared, equals, 273(x−4) 2 =27
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.
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