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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+16 x+63=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+16x+63=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+16 x+63=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+16x+63=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+16 x+63=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to solve.\newlineWe have the quadratic equation x2+16x+63=0x^2 + 16x + 63 = 0. We need to find two numbers that multiply to 6363 and add up to 1616.
  2. Find two numbers: Find two numbers that multiply to 6363 and add up to 1616.\newlineThe numbers 77 and 99 multiply to 6363 (7×9=637 \times 9 = 63) and add up to 1616 (7+9=167 + 9 = 16).
  3. Rewrite the quadratic equation: Rewrite the quadratic equation by splitting the middle term using the numbers found in Step 22.\newlinex2+7x+9x+63=0x^2 + 7x + 9x + 63 = 0
  4. Factor by grouping: Factor by grouping.\newlineGroup the terms to factor by common terms:\newline(x2+7x)+(9x+63)=0(x^2 + 7x) + (9x + 63) = 0\newlinex(x+7)+9(x+7)=0x(x + 7) + 9(x + 7) = 0
  5. Factor out the common binomial factor: Factor out the common binomial factor.\newline(x+7)(x+9)=0(x + 7)(x + 9) = 0
  6. Solve for x: Solve for x by setting each factor equal to zero.\newlinex+7=0x + 7 = 0 or x+9=0x + 9 = 0
  7. Solve the first equation: Solve the first equation for xx.x+7=0x + 7 = 0Subtract 77 from both sides:x=−7x = -7
  8. Solve the second equation: Solve the second equation for xx.x+9=0x + 9 = 0Subtract 99 from both sides:x=−9x = -9
  9. Write the solutions: Write the solutions in ascending order.\newlineThe solutions are x=−9x = -9 and x=−7x = -7.

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