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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+3x-28=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+3x−28=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+3 x-28=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Full solution

Q. Solve for x x . Enter the solutions from least to greatest.\newlinex2+3x−28=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+3 x-28=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Find two numbers: Find two numbers that multiply to −28-28 and add up to 33. The numbers that satisfy these conditions are 77 and −4-4 because 7×(−4)=−287 \times (-4) = -28 and 7+(−4)=37 + (-4) = 3.
  2. Write equation in factored form: Write the equation x2+3x−28=0x^2 + 3x - 28 = 0 in its factored form using the numbers found in the previous step. This gives us (x+7)(x−4)=0(x + 7)(x - 4) = 0.
  3. Solve for x (part 11): Set each factor equal to zero and solve for x. First, set x+7=0x + 7 = 0 and solve for x. Subtracting 77 from both sides gives us x=−7x = -7.
  4. Solve for x (part 22): Now, set x−4=0x - 4 = 0 and solve for x. Adding 44 to both sides gives us x=4x = 4.
  5. Final solution: We have found two solutions for x: −7-7 and 44. To answer the question prompt, we need to enter the solutions from least to greatest. The lesser value is −7-7, and the greater value is 44.

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