Question

question 6 of 10 which of the following are solutions to the equation below? check all that apply. 5x^{2}-2x + 16=4x^{2}+6x a -3 b. 4 c. 18 d. 6 e -6 f -4

Explanation:

Step1: Rearrange the equation

First, move all terms to one - side of the equation:
\[5x^{2}-2x + 16-(4x^{2}+6x)=0\]
\[5x^{2}-2x + 16 - 4x^{2}-6x=0\]
\[x^{2}-8x + 16 = 0\]

Step2: Factor the quadratic equation

The quadratic equation \(x^{2}-8x + 16\) is in the form of \(a^{2}-2ab + b^{2}=(a - b)^{2}\), where \(a=x\) and \(b = 4\).
So, \(x^{2}-8x + 16=(x - 4)^{2}=0\)

Step3: Solve for \(x\)

If \((x - 4)^{2}=0\), then \(x-4=0\), and \(x = 4\)

Answer:

B. 4