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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+x-30=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+x−30=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+x-30=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−30=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+x-30=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−30=0x^2 + x - 30 = 0. We need to find two numbers that multiply to −30-30 and add up to 11, which are the coefficients of the x2x^2 and xx terms, respectively.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineThe two numbers that multiply to −30-30 and add up to 11 are 66 and −5-5 because 6×(−5)=−306 \times (-5) = -30 and 6+(−5)=16 + (-5) = 1. Therefore, we can factor the quadratic equation as follows:\newlinex2+x−30=(x+6)(x−5)=0x^2 + x - 30 = (x + 6)(x - 5) = 0
  3. Solve for x: Solve for x by setting each factor equal to zero.\newlineFirst, set the first factor equal to zero:\newlinex+6=0x + 6 = 0\newlineSubtract 66 from both sides to solve for x:\newlinex=−6x = -6\newlineNext, set the second factor equal to zero:\newlinex−5=0x - 5 = 0\newlineAdd 55 to both sides to solve for x:\newlinex=5x = 5\newlineWe have found two solutions: x=−6x = -6 and x=5x = 5.
  4. Write the solutions: Write the solutions in ascending order.\newlineThe lesser value of xx is −6-6, and the greater value of xx is 55.

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