Find the real solution of the equation by graphing. 6x = 9 + x2
To find the real solutions of the equation 6x = 9 + x^2, we need to graph the equation and see where it intersects the x-axis.
First, we can rearrange the equation to form a quadratic equation:
x^2 - 6x + 9 = 0
Now we can graph this quadratic equation by finding its x-intercepts. To find the x-intercepts, we set y = 0 and solve for x:
x^2 - 6x + 9 = 0
(x - 3)(x - 3) = 0
(x - 3)^2 = 0
So, the equation has a double root at x = 3.
To graph this, we plot the point (3, 0) on the x-axis.
The graph of the equation is a parabola that opens upwards, and since it has a double root, it will touch the x-axis at x = 3 but not cross it.
Here is a visual representation of the graph:
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--+-----------------
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+----------
3
From the graph, we can see that the real solution to the equation is x = 3.