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{:[x^(2)+x-72=0],[(x+◻)^(2)=◻]:}

x2+x−72=0(x+□)2=□ \begin{array}{l}x^{2}+x-72=0 \\ (x+\square)^{2}=\square\end{array}

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Find higher derivatives of rational and radical functionsright chevron icon

Full solution

Q. x2+x−72=0(x+□)2=□ \begin{array}{l}x^{2}+x-72=0 \\ (x+\square)^{2}=\square\end{array}
  1. Factor the quadratic equation: First, we need to factor the quadratic equation x2+x−72=0x^2 + x - 72 = 0.
  2. Find suitable numbers: Looking for two numbers that multiply to −72-72 and add up to 11. After some trial and error, we find that 99 and −8-8 work because 9×−8=−729 \times -8 = -72 and 9+(−8)=19 + (-8) = 1.
  3. Write the factored equation: So we can write the equation as (x+9)(x−8)=0(x + 9)(x - 8) = 0.
  4. Set each factor equal: Now, we set each factor equal to zero: x+9=0x + 9 = 0 or x−8=0x - 8 = 0.
  5. Solve for x: Solving x+9=0x + 9 = 0 gives us x=−9x = -9.
  6. Final solutions: Solving x−8=0x - 8 = 0 gives us x=8x = 8.
  7. Final solutions: Solving x−8=0x - 8 = 0 gives us x=8x = 8.We found two values of xx that satisfy the equation: x=−9x = -9 and x=8x = 8.

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