Solving a quadratic equation by completing the square

Question

Solve the quadratic equation by completing the square.

First, choose the appropriate form and fill in the blanks with the correct numbers.

Then, solve the equation.

Answer 1

Let's solve your equation step-by-step.

x²−12x+29=0

Step 1: Subtract 29 from both sides.

x²−12x+29−29=0−29

x²−12x=−29

Step 2: The coefficient of -12x is -12.

Let b=-12.

Then we need to add (b/2)²=36 to both sides to complete the square.

Add 36 to both sides.

x²−12x+36=−29+36

x²−12x+36=7

Step 3: Factor left side.

(x−6)²=7

Step 4: Take square root.

x−6=±√7

Step 5: Add 6 to both sides.

x−6+6=6±√7

x=6±√7

Answer:

x=6+√7 or x=6−√7

Answer 2

x^2 -12x + 29 = 0

x^2 -12x = -29

take half of -12 and square it, then add that to both sides: (-12/2)^2 = (-6)^2 = 36

x^2 -12x + 6^2 = -29 + 6^2

x^2 -12x +36 = -29+36 = 7

(x-6)^2 = 7

take the square roots of both sides:

x-6 = + or - sqr7

x = 6 + or - sqr7

x= about 6 + or - 2.65

x = about 8.65 or 3.35