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Jamal solved the equation by completing the square.

SamJones  Jan 26, 2018
 #1
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Solve for x:

x^2 - 8 x + 14 = 0

 

Solve the quadratic equation by completing the square.

Subtract 14 from both sides:

x^2 - 8 x = -14

 

Take one half of the coefficient of x and square it, then add it to both sides.

Add 16 to both sides:

x^2 - 8 x + 16 = 2 [THIS STEP IS THE SECOND ONE OF YOUR 4 CHOICES]

 

Factor the left hand side.

Write the left hand side as a square:

(x - 4)^2 = 2

 

Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 4 = sqrt(2) or x - 4 = -sqrt(2)

 

Look at the first equation: Solve for x.

Add 4 to both sides:

x = 4 + sqrt(2) or x - 4 = -sqrt(2)

 

Look at the second equation: Solve for x.

Add 4 to both sides:

x = 4 + sqrt(2)       or         x = 4 - sqrt(2)

Guest Jan 26, 2018

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