Completing the Square Algebra Review

Solve 2+ 𝑥 2 =6𝑥 by completing the square 𝑥 2 −6𝑥=−2 𝑥 2 −6𝑥 + =−2 𝑥−3 2 = Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 2+ 𝑥 2 =6𝑥 by completing the square 𝑥 2 −6𝑥=−2 𝑥 2 −6𝑥+9=−2 +9 𝑥−3 2 =7 𝑥−3=± 7 𝑥=3± 7 Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 𝑥 2 +5𝑥−24=0 by completing the square 𝑥 2 +5𝑥=24 𝑥 2 +5𝑥 + ? ? =24 + ? ? 𝑥+ 5 2 2 = ? Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 𝑥 2 +5𝑥−24=0 by completing the square 𝑥 2 +5𝑥=24 𝑥 2 +5𝑥 + 25 4 = 96 4 + 25 4 𝑥+ 5 2 2 = 121 4 𝑥+ 5 2 =± 11 2 𝑥= 11 2 − 5 2 & − 11 2 − 5 2 𝑥=3 & −8 Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 5− 3 2 𝑥= 𝑥 2 by completing the square 5= 𝑥 2 + 3 2 𝑥 𝑥 2 + 3 2 𝑥+ ? ? =5+ ? ? 𝑥+ 3 4 2 = ? Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 5− 3 2 𝑥= 𝑥 2 by completing the square 5= 𝑥 2 + 3 2 𝑥 𝑥 2 + 3 2 𝑥+ 9 16 = 80 16 + 9 16 𝑥+ 3 4 2 = 89 16 𝑥+ 3 4 =± 89 4 𝑥= −3± 89 4 Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 4 𝑥 2 −3𝑥−1=0 by completing the square 𝑥 2 − 3 4 𝑥− 1 4 =0 𝑥 2 − 3 4 𝑥 + = 1 4 + 𝑥− 3 8 2 = Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Solve 4 𝑥 2 −3𝑥−1=0 by completing the square 𝑥 2 − 3 4 𝑥− 1 4 =0 𝑥 2 − 3 4 𝑥+ 9 64 = 16 64 + 9 64 𝑥− 3 8 2 = 25 64 𝑥− 3 8 =± 5 8 𝑥= 3±5 8 𝑥=1, − 1 4 Rewrite in the form 𝑥 2 +𝑏𝑥=𝑐 Add 𝑏 2 2 to both sides Factor & Simplify Square root both sides Solve for 𝑥

Questions? Completing the square is how we get the quadratic formula That will be our next review