Solution of $(4 x-16)^{\frac{1}{2}}=36 ?
x=5
x=13
x=20
x=328
Answer (2)
The solution to the equation ( 4 x − 16 ) 2 1 = 36 is x = 328 . This is found by squaring both sides, isolating x , and then solving the resulting equation.
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Square both sides of the equation: ( 4 x − 16 ) 2 1 = 36 becomes 4 x − 16 = 3 6 2 = 1296 .
Add 16 to both sides: 4 x = 1296 + 16 = 1312 .
Divide by 4: x = 4 1312 = 328 .
The solution is 328 .
Explanation
Understanding the Problem We are given the equation ( 4 x − 16 ) 2 1 = 36 and asked to find the value of x that satisfies it. This equation involves a square root, so our goal is to isolate x by first eliminating the square root.
Squaring Both Sides To eliminate the square root, we square both sides of the equation: (( 4 x − 16 ) 2 1 ) 2 = 3 6 2 This simplifies to: 4 x − 16 = 1296
Isolating the x Term Next, we want to isolate the term with x . We add 16 to both sides of the equation: 4 x − 16 + 16 = 1296 + 16 This simplifies to: 4 x = 1312
Solving for x Finally, we solve for x by dividing both sides of the equation by 4: 4 4 x = 4 1312 This gives us: x = 328
Final Answer Therefore, the solution to the equation ( 4 x − 16 ) 2 1 = 36 is x = 328 .
Examples
Imagine you are designing a square garden and want to determine the length of each side. If the area of the garden can be represented by the equation ( 4 x − 16 ) 2 1 = 36 , where x is related to the side length, solving for x will help you find the exact dimensions needed for your garden. This type of problem demonstrates how algebraic equations are used in practical scenarios to calculate real-world measurements and design layouts.
