chloelau91
Answered

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x^2-2x=5 solve by completing the square

Sagot :

Intriguing456

Answer:

x = ± sqrt(6) + 1

Step-by-step explanation:

[tex]x^2 - 2x = 5[/tex]

First, add half of -2 squared to both sides:

[tex]x^2 - 2x + (-\frac{2}{2})^2 = 5 + (-1)^2[/tex]

[tex]x^2 - 2x + 1 = 5 + 1[/tex]

[tex]x^2 - 2x + 1 = 6[/tex]

Then, factor the perfect square trinomial on the left:

[tex](x - 1)^2 = 6[/tex]

Finally, square root both sides:

[tex]\sqrt{(x - 1)^2} = \sqrt{6}[/tex]

[tex]x - 1 = \sqrt{6}[/tex] or [tex]x - 1 = -\sqrt{6}[/tex]

x = ± sqrt(6) + 1

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