Solve by Factoring 25x^2+16=40x

Problem

25*x^2+16=40*x

Solution

1. Rearrange the equation into standard quadratic form a*x^2+b*x+c=0 by subtracting 40*x from both sides.

25*x^2−40*x+16=0

2. Identify the structure of the trinomial as a potential perfect square trinomial, noting that 25*x^2=(5*x)^2 and 16=4^2

25*x^2−40*x+16=(5*x)^2−2*(5*x)*(4)+4^2

3. Factor the expression using the perfect square trinomial formula a^2−2*a*b+b^2=(a−b)^2

(5*x−4)^2=0

4. Solve for x by taking the square root of both sides and isolating the variable.

5*x−4=0

5*x=4

x=4/5

Final Answer

x=4/5

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