Answer: [tex]\bold{x = -4\pm \sqrt{29}}[/tex]
Step-by-step explanation:
Step 1: Create a perfect square: Add the value to both sides
x² + 8x + 16 = 13 + 16
↓ ↑ ↑
[tex]\dfrac{8}{2} = (4)^2[/tex]
Step 2: Factor left side so it is a perfect square and simplify right side:
[tex](x + 4)^2 = 29[/tex]
Step 3: Take the square root of both sides
[tex]x + 4 = \pm \sqrt{29}[/tex]
Step 4: Solve for x:
[tex]x = -4\pm \sqrt{29}[/tex]
Answer:
x = - 4 ± [tex]\sqrt{29}[/tex]
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 = ± [tex]\sqrt{29}[/tex] ← note plus or minus
subtract 4 from both sides
x = - 4 ± [tex]\sqrt{29}[/tex] ← exact solutions
