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Sagot :
[tex]x^2=-8x-7[/tex]
First we rewrite it to have an equation equal to zero:
[tex]x^2+8x+7=0[/tex]To complete the square we have to consider that a perfect square looks like:
[tex](x\pm c)^{2}=x^2\pm2xc+c^2[/tex]In this equation we have in the second term 8x, so comparing it to the perfect square we have that c must be 4:
[tex]x^2+2\cdot x\cdot4+7=0[/tex]If the last term of a perfect square is c², we should have 16 instead of 7. To complete the square we have to add and substract 16:
[tex]x^2+2\cdot x\cdot4+16-16+7=0[/tex]Note that if we do that the equation remains the same.
Now if we look at the first 3 terms we can see a perfect square:
[tex]\begin{gathered} (x^2+2\cdot x\cdot4+16)-16+7=0 \\ (x+4)^{2}-9=0 \end{gathered}[/tex]And now we add 9 on both sides of the equation:
[tex]\begin{gathered} (x+4)^2-9+9=0+9 \\ (x+4)^2=9 \end{gathered}[/tex]The equation rewritten in complete square form is (x + 4)² = 9
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