solve this quadratic equation by completing the square.\n$x^{2}+8x = 10$\na. $x=-8pmsqrt{26}$\nb…

solve this quadratic equation by completing the square.\n$x^{2}+8x = 10$\na. $x=-8pmsqrt{26}$\nb. $x=-8pmsqrt{10}$\nc. $x=-4pmsqrt{26}$\nd. $x=-4pmsqrt{10}$

solve this quadratic equation by completing the square.\n$x^{2}+8x = 10$\na. $x=-8pmsqrt{26}$\nb. $x=-8pmsqrt{10}$\nc. $x=-4pmsqrt{26}$\nd. $x=-4pmsqrt{10}$

Answer

Explanation:

Step1: Add square of half of coefficient of x

The coefficient of $x$ is $8$. Half of it is $4$ and its square is $16$. Add $16$ to both sides of the equation $x^{2}+8x = 10$. $x^{2}+8x + 16=10 + 16$

Step2: Rewrite left - hand side as a perfect square

The left - hand side $x^{2}+8x + 16=(x + 4)^{2}$, and the right - hand side is $26$. So, $(x + 4)^{2}=26$.

Step3: Take square root of both sides

$x+4=\pm\sqrt{26}$

Step4: Solve for x

Subtract $4$ from both sides: $x=-4\pm\sqrt{26}$

Answer:

C. $x=-4\pm\sqrt{26}$