Question

Solve by completing the square x²+8x=13

Answer 1

Answer:   $\bold{x = -4\pm \sqrt{29}}$

Step-by-step explanation:

Step 1: Create a perfect square:  Add the value to both sides

x² + 8x +  16   = 13 +  16  

       ↓       ↑                 ↑

      $\dfrac{8}{2} = (4)^2$

Step 2: Factor left side so it is a perfect square and simplify right side:

$(x + 4)^2 = 29$

Step 3: Take the square root of both sides

$x + 4 = \pm \sqrt{29}$

Step 4: Solve for x:

$x = -4\pm \sqrt{29}$

Answer 2

Answer:

x = - 4 ± $\sqrt{29}$

Step-by-step explanation:

the coefficient of the x² term is 1 as required

to complete the square

add (half the coefficient of the x-term )² to both sides

x² +2(4)x + 16 = 13 + 16

(x + 4)² = 29 ( take the square root of both sides )

x + 4 = ± $\sqrt{29}$ ← note plus or minus

subtract 4 from both sides

x = - 4 ± $\sqrt{29}$ ← exact solutions