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Find the zeros of the function. Enter the solutions from least to greatest. f(x)=(x+6)^(2)-49 lesser x= greater x=

Find the zeros of the function. Enter the solutions from least to greatest.\newlinef(x)=(x+6)2−49f(x)=(x+6)^{2}-49\newlinelesser x=x= greater 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+6)2−49f(x)=(x+6)^{2}-49\newlinelesser x=x= greater x=x=
  1. Find Zeros: Set the function equal to zero to find the zeros.\newlinef(x)=(x+6)2−49=0f(x) = (x+6)^2 - 49 = 0
  2. Factor the Equation: Factor the equation using the difference of squares.\newline(x+6)2−49=(x+6+7)(x+6−7)(x+6)^2 - 49 = (x+6+7)(x+6-7)\newline(x+6+7)(x+6−7)=(x+13)(x−1)(x+6+7)(x+6-7) = (x+13)(x-1)
  3. Solve for x: Set each factor equal to zero and solve for x.\newlinex+13=0x+13 = 0 or x−1=0x-1 = 0\newlineFor x+13=0x+13 = 0: x=−13x = -13\newlineFor x−1=0x-1 = 0: x=1x = 1
  4. Write Solutions: Write the solutions in ascending order.\newlinelesser x=−13x = -13\newlinegreater x=1x = 1

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