Start by identifying the values of a, b, and c. Be sure that all of the terms of are on the same side and in the correct order for the standard form of a quadratic function.
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Practice makes perfect
To solve the given equation by factoring, we will start by identifying the values of a, b, and c.
25a^2 - 40a=-16 ⇔ 25a^2 + ( - 40)a + 16=0
Notice that this equation follows a special pattern. It can be factored as a perfect square trinomial.
Let's rewrite the given expression as perfect square trinomial.
(5a)^2-(2* 5a* 4)+4^2=0 ⇕ (5a-4)^2=0
Now we are ready to use the Zero Product Property.
We found that the solution to the given equation is a= 45. To check our answer, we will graph the related functions y=25x^2-40x+16 and y=(5x-4)^2 in the same coordinate plane using a graphing calculator. Note that in the calculator we will use the variable x instead of a.
We see that only one graph appears. This means that both graphs coincide. We can see that the x-intercept is 45. Therefore, our solution is correct. âś“
