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

Solve for x x . Enter the solutions from least to greatest.\newlinex2−x−12=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-x-12=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−x−12=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-x-12=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−x−12=0x^2 - x - 12 = 0. We need to find two numbers that multiply to −12-12 and add up to −1-1, the coefficient of xx.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineThe two numbers that multiply to −12-12 and add up to −1-1 are −4-4 and 33 because (−4)×3=−12(-4) \times 3 = -12 and (−4)+3=−1(-4) + 3 = -1. So we can write the equation as (x−4)(x+3)=0(x - 4)(x + 3) = 0.
  3. Solve for x using the factored form: Solve for x using the factored form.\newlineSet each factor equal to zero and solve for x:\newlinex−4=0x - 4 = 0 or x+3=0x + 3 = 0.
  4. Find the first solution: Find the first solution.\newlineSolve x−4=0x - 4 = 0 by adding 44 to both sides:\newlinex=4x = 4.
  5. Find the second solution: Find the second solution.\newlineSolve x+3=0x + 3 = 0 by subtracting 33 from both sides:\newlinex=−3x = -3.
  6. List the solutions in ascending order: List the solutions in ascending order.\newlineThe lesser value of xx is −3-3, and the greater value of xx is 44.

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