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{:[" 12. "x^(2)+16 x+55=3],[x^(2)+16 x=-55],[+64quad+64quad(8)^(2)=64],[x^(2)+16 x+64=12],[sqrt((x+8)^(2))=sqrt12],[x+8=2sqrt3quad x+8=-2sqrt3]:} 9x^(2)=18 x+40

 12. x2+16x+55=3x2+16x=−55+64+64(8)2=64x2+16x+64=12(x+8)2=12x+8=23x+8=−23 \begin{array}{l} \text { 12. } x^{2}+16 x+55=3 \\ x^{2}+16 x=-55 \\ +64 \quad+64 \quad(8)^{2}=64 \\ x^{2}+16 x+64=12 \\ \sqrt{(x+8)^{2}}=\sqrt{12} \\ x+8=2 \sqrt{3} \quad x+8=-2 \sqrt{3} \end{array} \newline1414. 9x2=18x+40 9 x^{2}=18 x+40

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Q.  12. x2+16x+55=3x2+16x=−55+64+64(8)2=64x2+16x+64=12(x+8)2=12x+8=23x+8=−23 \begin{array}{l} \text { 12. } x^{2}+16 x+55=3 \\ x^{2}+16 x=-55 \\ +64 \quad+64 \quad(8)^{2}=64 \\ x^{2}+16 x+64=12 \\ \sqrt{(x+8)^{2}}=\sqrt{12} \\ x+8=2 \sqrt{3} \quad x+8=-2 \sqrt{3} \end{array} \newline1414. 9x2=18x+40 9 x^{2}=18 x+40
  1. Identify Function Types: Identify the types of functions.\newlinef(x)=2x+9f(x) = 2x + 9 is a linear function.\newlineg(x)=2xg(x) = 2^x is an exponential function.
  2. Compare Growth Rates: Compare the growth rates. Exponential functions grow faster than linear functions.
  3. Determine Exceeding Function: Determine which function will exceed the other.\newlineAs xx gets larger, g(x)=2xg(x) = 2^x will eventually exceed f(x)=2x+9f(x) = 2x + 9.
  4. Solve Quadratic Equation: New Math Problem: Solve 9x2=18x+409x^2 = 18x + 40.
  5. Set Equation to Zero: Subtract 18x18x and 4040 from both sides to set the equation to zero.\newline9x2−18x−40=09x^2 - 18x - 40 = 0
  6. Factor Quadratic Equation: Factor the quadratic equation.\newline(3x+4)(3x−10)=0(3x + 4)(3x - 10) = 0

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