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Sagot :
We must solve for x the following equation:
[tex]x^2+6x+9=25.[/tex]1) We pass the +25 on the right to left as -25:
[tex]\begin{gathered} x^2+6x+9-25=0, \\ x^2+6x-16=0. \end{gathered}[/tex]2) Now, we can rewrite the equation in the following form:
[tex]x\cdot x+8\cdot x-2\cdot x-2\cdot8=0.[/tex]3) Factoring the last expression, we have:
[tex]x\cdot(x+8)-2\cdot(x+8)=0.[/tex]Factoring the (x+8) in each term:
[tex](x-2)\cdot(x+8)=0.[/tex]4) By replacing x = 2 or x = -8 in the last expression, we see that the equation is satisfied. So the solutions of the equation are:
[tex]\begin{gathered} x=2, \\ x=-8. \end{gathered}[/tex]Answer
The solutions are:
• x = 2
,• x = -8
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