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
[tex]\huge\text{Hey there!}[/tex]
[tex]\textbf{Assuming you meant: }\mathsf{(2x + 5)^2 = 4x(x + 5) + 25}[/tex]
[tex]\textbf{If so, simplify both sides of your equation you're working with}[/tex]
[tex]\mathsf{ 4x^2 + 20x + 25 = 4x^2 + 20x + 25}[/tex]
[tex]\textbf{SUBTRACT }\rm{\bf 4x^2}\text{ \bf to BOTH of the SIDES}[/tex]
[tex]\mathsf{4x^2 + 20x + 25 - 4x^2 = 4x^2 + 20x + 25 - 4x^2}[/tex]
[tex]\textbf{Simplify it!}[/tex]
[tex]\mathsf{20x + 25 = 20x + 25}[/tex]
[tex]\textbf{SUBTRACT 20x to BOTH of the SIDES}[/tex]
[tex]\mathsf{20x + 25 - 20x = 20x + 25 - 20x}[/tex]
[tex]\large\textbf{SIMPLIFY IT! (as well)}[/tex]
[tex]\mathsf{25 = 25}[/tex]
[tex]\textbf{SUBTRACT 25 to BOTH of the SIDES}[/tex]
[tex]\mathsf{25 - 25 = 25 - 25}[/tex]
[tex]\textbf{Lastly, SIMPLIFY THAT!}[/tex]
[tex]\textbf{We get: }\mathsf{0 = 0}[/tex]
[tex]\large\textsf{This means that your \boxed{\textsf{solutions}} are \bf REAL NUMBERS.}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }\\\boxed{\mathsf{All\ \underline{\underline{REAL\ NUMBERS}}\ are\ solutions.}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
