Final answer:
To solve the equation 2x^2=2, simplify it to x^2=1. Find the roots by taking the square root of both sides or graphing the function f(x)=x^2-1, which shows x-intercepts at x=1 and x=-1.
Step-by-step explanation:
To find the solutions of the equation 2x^2=2, we first divide both sides by 2 to simplify the equation to x^2=1. This is a quadratic equation in standard form ax^2+bx+c=0, where a=1, b=0, and c=-1.
One way to find the roots is to graph the related function f(x)=x^2-1.
The roots of the equation are the x-intercepts of the graph, which are the points where the graph crosses the x-axis.
Since x^2=1, we can take the square root of both sides to obtain x=±1.
Thus, the solutions to the equation are x=1 and x=-1.
These are the points where the graph of y=x^2 crosses the value of y=1, confirming the roots graphically as well.