Question

What number must you add to complete the square? x^2+8x=9

Answer 1

• x²+8x+9

We know

• (a+b)²=a²+2ab+b²

To get 2ab satisfied

• 2ab=8x
• 2x(b)=8x
• b=4
• b²=16

16 must be added on both sides to get (x+4)²

Answer 2

`\huge\textsf{Hey there!}`

`\mathsf{x^2 + 8x = 9}`

`\large\textsf{SUBTRACT 9 to BOTH SIDES}`

`\mathsf{x^2 + 8x - 9 = 9 - 9}`

`\mathsf{x^2 + 8x - 9 = 0}`

`\large\textsf{FACTOR the LEFT SIDE of the EQUATION}`

`\mathsf{(x - 1)(x + 9) = 0}`

`\large\textsf{SET the FACTORS to EQUAL 0}`

`\mathsf{x - 1 = 0 \ OR \ x + 9 = 0}`

`\large\textsf{Simplify above and you have your answer to the question above (also}\\\large\textsf{known as the results for your x-values)}`

`\boxed{\boxed{\large\textsf{Answer: \huge \bf x = 1 or x = -9}}}\huge\checkmark`

`\large\textsf{But, your overall answer should be:}`

`\huge\boxed{\textbf{ADD \underline{16} to both sides}}`

`\large\textsf{Because, you had to break down x}\mathsf{^2}\large\textsf{ to (x + 4)(x + 4) or you could}\\\large\textsf{simply say (x + 2)}\mathsf{^2.}`

`\large\textsf{Good luck on your assignment and enjoy your day!}`

~
`\frak{Amphitrite1040:)}`