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Solve for x. Enter the solutions from least to greatest. {:[5x^(2)+15 x-50=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline5x2+15x−50=0 lesser x=□ greater x=□ \begin{array}{l} 5 x^{2}+15 x-50=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.\newline5x2+15x−50=0 lesser x=□ greater x=□ \begin{array}{l} 5 x^{2}+15 x-50=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Write Quadratic Equation: Write down the given quadratic equation.\newline5x2+15x−50=05x^2 + 15x - 50 = 0
  2. Factor Out GCF: Factor out the greatest common factor (GCF) from the quadratic equation.\newlineThe GCF of 5x25x^2, 15x15x, and −50-50 is 55.\newline5(x2+3x−10)=05(x^2 + 3x - 10) = 0
  3. Factor Quadratic Expression: Factor the quadratic expression inside the parentheses.\newlineWe need to find two numbers that multiply to −10-10 and add up to 33.\newlineThe numbers 55 and −2-2 satisfy these conditions because 5×−2=−105 \times -2 = -10 and 5+(−2)=35 + (-2) = 3.\newlineSo, we can write the factored form as:\newline5(x+5)(x−2)=05(x + 5)(x - 2) = 0
  4. Solve for x: Set each factor equal to zero and solve for x.\newlineFirst factor:\newlinex+5=0x + 5 = 0\newlineSubtract 55 from both sides:\newlinex=−5x = -5\newlineSecond factor:\newlinex−2=0x - 2 = 0\newlineAdd 22 to both sides:\newlinex=2x = 2
  5. Write Solutions in Ascending Order: Write down 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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