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Find the zeros of the function. Enter the solutions from least to greatest. f(x)=(x+2)^(2)-16 lesser x= ◻ greater x= ◻

Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x+2)2−16f(x)=(x+2)^{2}-16\newlinelesser x=□ x= \square \newlinegreater x=□ x= \square

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One-step inequalities: word problemsright chevron icon

Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x+2)2−16f(x)=(x+2)^{2}-16\newlinelesser x=□ x= \square \newlinegreater x=□ x= \square
  1. Set Function Equal Zero: Set the function equal to zero to find its zeros. f(x)=(x+2)2−16=0f(x) = (x+2)^2 - 16 = 0
  2. Add 1616 Isolate Term: Add 1616 to both sides of the equation to isolate the squared term.\newline(x+2)2=16(x+2)^2 = 16
  3. Take Square Root Solve: Take the square root of both sides of the equation to solve for xx.(x+2)2=±16\sqrt{(x+2)^2} = \pm\sqrt{16}x+2=±4x + 2 = \pm4
  4. Solve for x: Solve for x by subtracting 22 from both sides of the equation for both the positive and negative cases.\newlineFor the positive case:\newlinex+2−2=4−2x + 2 - 2 = 4 - 2\newlinex=2x = 2\newlineFor the negative case:\newlinex+2−2=−4−2x + 2 - 2 = -4 - 2\newlinex=−6x = -6

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