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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-x-90=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−x−90=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-x-90=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for x x . Enter the solutions from least to greatest.\newlinex2−x−90=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-x-90=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify Quadratic Equation: Identify the quadratic equation to solve.\newlineThe given quadratic equation is x2−x−90=0x^2 - x - 90 = 0. We need to find two numbers that multiply to −90-90 and add up to −1-1, the coefficient of xx.
  2. Factor the Equation: Factor the quadratic equation.\newlineTo factor x2−x−90=0x^2 - x - 90 = 0, we look for two numbers that multiply to −90-90 and add to −1-1. The numbers −10-10 and 99 satisfy these conditions because −10×9=−90-10 \times 9 = -90 and −10+9=−1-10 + 9 = -1.\newlineSo, we can write the equation as (x−10)(x+9)=0(x - 10)(x + 9) = 0.
  3. Solve for x: Solve for x using the zero product property.\newlineIf (x−10)(x+9)=0(x - 10)(x + 9) = 0, then either x−10=0x - 10 = 0 or x+9=0x + 9 = 0.\newlineSolving x−10=0x - 10 = 0 gives us x=10x = 10.\newlineSolving x+9=0x + 9 = 0 gives us x=−9x = -9.
  4. Write Solutions in Ascending Order: Write the solutions in ascending order.\newlineThe lesser value of xx is −9-9, and the greater value of xx is 1010.

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