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Solve by completing the square (Show all work)
x2 – 10x + 10 = 35

Please help!

User Whitenexx
by
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1 Answer

6 votes

Answer:

x=5+5√2; x=5-5√2

Explanation:

To complete the square we need to turn part of the equation into a perfect square trinomial. Remember, in any equation we can do anything we like to the numbers as long as both sides stay equal.

First, let's subtract 10 from both sides.

x^2-10x=25

This does not factor, so we need to turn it into a perfect square trinomial by adding the quantity equal to (b/2)^2. In this case, (b/2)^2 is 25.

x^2−10x+25=25+25

IMPORTANT: You must keep the sides of the equation equal, so we added a 25 to the right side as well to keep the equation true.

From here we can factor, simplify and find our zeroes.

(x-5)(x-5)=50

(x-5)^2=50

x-5=±√50

x=5±√50

√50=5√2

So our final answer is:

x=5+5√2; x=5-5√2

HTH :)

User Kenesia
by
4.7k points