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To solve the equation −x^2+5x = −x+5, we need to set the two expressions equal to each other:
−x^2+5x = −x+5
Now, we can simplify the equation:
0 = x^2 - 6x + 5
This equation can be factored into:
0 = (x - 1)(x - 5)
Setting each factor equal to zero gives us the solutions x = 1 and x = 5.
Looking at the table, we see that the value of k that corresponds to x = 1 in the second table is 4. Therefore, the value of k that will be a solution to the equation is:
k = 4