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Solve for x. Enter the solutions from least to greatest. -x^(2)-8=-33 lesser x= greater x=

Solve for x x .\newlineEnter the solutions from least to greatest.\newline−x2−8=−33 -x^{2}-8=-33 \newlinelesser x= x= \newlinegreater x= x=

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Full solution

Q. Solve for x x .\newlineEnter the solutions from least to greatest.\newline−x2−8=−33 -x^{2}-8=-33 \newlinelesser x= x= \newlinegreater x= x=
  1. Rewrite equation to isolate x2x^2: First, let's rewrite the equation to isolate the x2x^2 term on one side.\newline−x2−8=−33-x^2 - 8 = -33\newlineAdd 88 to both sides to get:\newline−x2=−33+8-x^2 = -33 + 8\newline−x2=−25-x^2 = -25
  2. Get rid of negative sign: Now, we need to get rid of the negative sign in front of x2x^2. We can do this by multiplying both sides of the equation by −1-1.\newline−x2×−1=−25×−1-x^2 \times -1 = -25 \times -1\newlinex2=25x^2 = 25
  3. Take square root of both sides: Next, we take the square root of both sides to solve for xx. Remember that taking the square root of a number gives us two solutions: one positive and one negative.\newlinex2=±25\sqrt{x^2} = \pm\sqrt{25}\newlinex=±5x = \pm5
  4. Two solutions for x: We now have two solutions for x. The lesser value is −5-5 and the greater value is 55.\newlinelesser x=−5x = -5\newlinegreater x=5x = 5

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