Question

Solve the equation 4x° - 32x + 64 = 0.

Answer 1

- The solution steps are given below:

`\begin{gathered} 4x^2-32x+64=0 \\ \text{ Factorize 4 out since all coefficient and constant are multiples of 4} \\ \\ 4(x^2-8x+16)=0 \\ \\ \text{ Divide both sides by 4} \\ \\ x^2-8x+16=0 \\ \text{ We can rewrite the x-term as follows:} \\ -8x=-4x-4x \\ \text{ Thus, we have:} \\ \\ x^2-4x-4x+16=0 \\ \text{ Factorize} \\ x(x-4)-4(x-4)=0 \\ (x-4)\text{ is common to both terms, so we can factorize it out again,} \\ \\ (x-4)(x-4)=0 \\ \\ \text{ Thus, we can say that} \\ x-4=0 \\ \text{ Add 4 to both sides} \\ x=4 \end{gathered}`

Final Answer

x = 4