Question

Solve this quadratic equation by completing the square is it a b c or dx² + 8x= 10A. x=-8± √10B. x=-4 ± √26C. x= -8 ± √26D. x=-4 ± √10

Answer 1

Given the quadratic equation below

`x²+8x=10`

Solving the quadratic equation by completing the square method;

`\begin{gathered} Where \\ b=8 \\ Add\text{ }((b)/(2))^2\text{ to both sides of the equation} \\ ((8)/(2))^2=4^2=16 \\ x^2+8x+4^2=10+16 \\ (x+4)^2=26 \end{gathered}`

Then find the square root of both sides

`\begin{gathered} √((x+4)^2)=\pm√(26) \\ x+4=\pm√(26) \\ Subtract\text{ 4 from both sides} \\ x+4-4=-4\pm√(26) \\ x=-4\pm√(26) \end{gathered}`

Thus;

`x=-4\pm√(26)`

Hence, the answer is B