Question

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

Answer 1

Answer: x = -5/2 and x = -3/2

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

Answer 2

`\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`

~
`\frak{Amphitrite1040:)}`