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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+12 x+32=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+12x+32=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+12 x+32=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Q. Solve for x x . Enter the solutions from least to greatest.\newlinex2+12x+32=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+12 x+32=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineWe have the quadratic equation x2+12x+32=0x^2 + 12x + 32 = 0.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 3232 and add up to 1212. The numbers 44 and 88 satisfy these conditions because 4×8=324 \times 8 = 32 and 4+8=124 + 8 = 12.\newlineSo, we can write the equation as (x+4)(x+8)=0(x + 4)(x + 8) = 0.
  3. Solve for x using zero product property: Solve for x using the zero product property.\newlineIf (x+4)(x+8)=0(x + 4)(x + 8) = 0, then either x+4=0x + 4 = 0 or x+8=0x + 8 = 0.\newlineFor x+4=0x + 4 = 0:\newlineSubtract 44 from both sides to solve for x.\newlinex+4−4=0−4x + 4 - 4 = 0 - 4\newlinex=−4x = -4\newlineFor x+8=0x + 8 = 0:\newlineSubtract 88 from both sides to solve for x.\newlinex+8−8=0−8x + 8 - 8 = 0 - 8\newlinex=−8x = -8
  4. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe solutions are x=−8x = -8 and x=−4x = -4, with −8-8 being the lesser value and −4-4 being the greater value.

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