Final answer:
To solve 2x^2+20x=10, one must first divide by 2, then add the square of half the coefficient of x (which is 25) to both sides to complete the square, resulting in (x+5)^2=30. Solving for x gives x = -5 ± √30.
Step-by-step explanation:
The student asked how to solve the equation 2x^2+20x=10 by completing the square. To complete the square, one must rearrange the equation to form a perfect square trinomial on one side of the equation. First, let's divide everything by 2 to simplify the equation: x^2+10x=5. Then, to form a perfect square on the left, you add the square of half the coefficient of x to both sides, which is (10/2)^2 = 25. Thus, the equation becomes x^2+10x+25=5+25 or (x+5)^2=30. Taking the square root of both sides gives us x+5=±√30, and finally, isolating x yields two solutions: x = -5 + √30 or x = -5 - √30.