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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+3x-10=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+3x−10=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+3 x-10=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+3x−10=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+3 x-10=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+3x−10=0x^2 + 3x - 10 = 0. We need to find two numbers that multiply to −10-10 and add up to 33.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineThe two numbers that multiply to −10-10 and add up to 33 are 55 and −2-2, because 5×(−2)=−105 \times (-2) = -10 and 5+(−2)=35 + (-2) = 3.\newlineSo we can write the equation as (x+5)(x−2)=0(x + 5)(x - 2) = 0.
  3. Solve for x using zero product property: Solve for x using the zero product property.\newlineIf (x+5)(x−2)=0(x + 5)(x - 2) = 0, then either x+5=0x + 5 = 0 or x−2=0x - 2 = 0.\newlineFor x+5=0x + 5 = 0:\newlinex=−5x = -5\newlineFor x−2=0x - 2 = 0:\newlinex=2x = 2
  4. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe lesser value of xx is −5-5, and the greater value of xx is 22.

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