Question

Prove the equation (2x+5)2 = 4x (x + 5) +25

Answer 1

$\huge\text{Hey there!}$

$\textbf{Assuming you meant: }\mathsf{(2x + 5)^2 = 4x(x + 5) + 25}$

$\textbf{If so, simplify both sides of your equation you're working with}$

$\mathsf{ 4x^2 + 20x + 25 = 4x^2 + 20x + 25}$

$\textbf{SUBTRACT }\rm{\bf 4x^2}\text{ \bf to BOTH of the SIDES}$

$\mathsf{4x^2 + 20x + 25 - 4x^2 = 4x^2 + 20x + 25 - 4x^2}$

$\textbf{Simplify it!}$

$\mathsf{20x + 25 = 20x + 25}$

$\textbf{SUBTRACT 20x to BOTH of the SIDES}$

$\mathsf{20x + 25 - 20x = 20x + 25 - 20x}$

$\large\textbf{SIMPLIFY IT! (as well)}$

$\mathsf{25 = 25}$

$\textbf{SUBTRACT 25 to BOTH of the SIDES}$

$\mathsf{25 - 25 = 25 - 25}$

$\textbf{Lastly, SIMPLIFY THAT!}$

$\textbf{We get: }\mathsf{0 = 0}$

$\large\textsf{This means that your \boxed{\textsf{solutions}} are \bf REAL NUMBERS.}$

$\huge\textsf{Therefore, your answer should be: }\\\boxed{\mathsf{All\ \underline{\underline{REAL\ NUMBERS}}\ are\ solutions.}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$

Answer 2

Answer:  x = -5/2 and x = -3/2

Step-by-step explanation:

(2x + 5)2 = 4x (x + 5) +25

   4x + 10 = 4x² + 20x + 25

   [minus 4x on both sides.]

            10 = 4x² + 16x + 25

   [minus 10 on both sides.]

            0 = 4x² + 16x + 15

ac = 4(15) = 60,then find the factors that add up to 16, which is 6 and 10.

            0 = 4x² + 6x + 10x + 15

            0 = 2x(2x + 3) + 5(2x + 3)

            0 = (2x + 5)(2x + 3)

2x + 5 = 0                                 2x + 3 = 0

       2x = -5                                    2x = -3

         x = -5/2                                    x = -3/2