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Find the zeros of the function. Enter the solutions from least to greatest. f(x)=(x-7)^(2)-64 lesser x= greater x=

Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−7)2−64 f(x)=(x-7)^{2}-64 \newlinelesser x= x= \newlinegreater x= x=

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Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x−7)2−64 f(x)=(x-7)^{2}-64 \newlinelesser x= x= \newlinegreater x= x=
  1. Step 11: Solve the equation: To find the zeros of the function, we need to solve the equation (x−7)2−64=0(x - 7)^2 - 64 = 0 for xx.
  2. Step 22: Isolate the squared term: First, we add 6464 to both sides of the equation to isolate the squared term:\newline(x−7)2−64+64=0+64(x - 7)^2 - 64 + 64 = 0 + 64\newline(x−7)2=64(x - 7)^2 = 64
  3. Step 33: Take the square root: Next, we take the square root of both sides of the equation to solve for x−7x - 7. Remember that taking the square root of a number yields two solutions, one positive and one negative:\newline(x−7)2=±64\sqrt{(x - 7)^2} = \pm\sqrt{64}\newlinex−7=±8x - 7 = \pm8
  4. Step 44: Set up two equations: Now we have two equations to solve for xx:\begin{enumerate}\item x−7=8x - 7 = 8\item x−7=−8x - 7 = -8\end{enumerate}
  5. Step 55: Solve the first equation: Solving the first equation for xx:x−7=8x - 7 = 8x=8+7x = 8 + 7x=15x = 15
  6. Step 66: Solve the second equation: Solving the second equation for xx:x−7=−8x - 7 = -8x=−8+7x = -8 + 7x=−1x = -1
  7. Step 77: Find the zeros: We have found the two zeros of the function:\newlinelesser x=−1x = -1\newlinegreater x=15x = 15

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