Question

solve for ( x ) in the equation ( x^2 - 10x + 25 = 35 ).
( circ ) ( x = 5 pm 2sqrt{5} )
( circ ) ( x = 5 pm sqrt{35} )
( circ ) ( x = 10 pm 2sqrt{5} )
( circ ) ( x = 10 pm sqrt{35} )

Explanation:

Step1: Rewrite equation to isolate constant

$x^2 - 10x + 25 - 25 = 35 - 25$
$x^2 - 10x = 10$

Step2: Complete the square

$x^2 - 10x + 25 = 10 + 25$
$(x - 5)^2 = 35$

Step3: Take square root of both sides

$x - 5 = \pm \sqrt{35}$

Step4: Solve for x

$x = 5 \pm \sqrt{35}$

Answer:

$x = 5 \pm \sqrt{35}$ (corresponding to the second option: $x=5\pm\sqrt{35}$)