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Solve for x. Enter the solutions from least to greatest. {:[4x^(2)+4x-168=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline4x2+4x−168=0 lesser x=□ greater x=□ \begin{array}{l} 4 x^{2}+4 x-168=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.\newline4x2+4x−168=0 lesser x=□ greater x=□ \begin{array}{l} 4 x^{2}+4 x-168=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Step 11: Factoring Attempt: We have the quadratic equation 4x2+4x−168=04x^2 + 4x - 168 = 0. To solve for xx, we can first try to factor the quadratic, or use the quadratic formula. Let's start by attempting to factor.
  2. Step 22: Simplifying the Equation: To make factoring easier, we can divide the entire equation by 44 to simplify it, since all terms are divisible by 44. This gives us x2+x−42=0x^2 + x - 42 = 0.
  3. Step 33: Finding the Numbers: Now we need to find two numbers that multiply to −42-42 and add up to 11 (the coefficient of xx). The numbers that satisfy these conditions are 77 and −6-6, because 7×(−6)=−427 \times (-6) = -42 and 7+(−6)=17 + (-6) = 1.
  4. Step 44: Rewriting the Equation: We can now rewrite the quadratic equation as (x+7)(x−6)=0(x + 7)(x - 6) = 0.
  5. Step 55: Solving for the First Factor: Setting each factor equal to zero gives us the solutions for x. For the first factor, x+7=0x + 7 = 0, we solve for x by subtracting 77 from both sides, which gives us x=−7x = -7.
  6. Step 66: Solving for the Second Factor: For the second factor, x−6=0x - 6 = 0, we solve for xx by adding 66 to both sides, which gives us x=6x = 6.
  7. Step 77: Final Solutions: We have found two solutions: x=−7x = -7 and x=6x = 6. To answer the question prompt, we list the solutions from least to greatest: −7,6-7, 6.

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