ALGEBRA I SECTION 9 5 COMPLETING THE SQUARE
ALGEBRA I @ SECTION 9 -5 : COMPLETING THE SQUARE
1) Chloe planted daylilies on a square piece of land with an area of 49 square feet. She wants to plant petunias around the daylilies to form a border whose area is 72 square feet. What length should she make the sides of the outer square? a SOLUTION : Draw a picture. daylilies x 2 – 49 = 72 x 2 = 121 x Since length can’t be negative, the only answer that works is 11. x
Use the square root method to solve each quadratic equation. Remember, every quadratic equation has 2 solutions. Use 2) x 2 = 49 ANSWERS : -7, 7
3) 2 x 2 – 300 = 0 ANSWERS :
4) (x + 3)2 = 400 ANSWERS : -23, 17
Quadratic Equation : ax 2 + bx + c = 0 quadratic term linear term constant term
Solve by completing the square. 5 x 2 + 10 x – 15 = 0 5 x 2 + 10 x = 15 constant to one side, variables to the other. Get the coefficient of the quadratic term to be 1 x 2 + 2 x =3 x 2 + 2 x + 1 =3+1 (x + 1)2 =4 Divide the coefficient of the linear term by 2, square the result, add to both sides. Simplify. Make the
(x + 1)2 =4 Take the square root of both sides. Use when you take the square root of both sides. x = -1 + 2 OR x = -1 - 2 x=1 OR x = -3
Solve by completing the square. 5) y 2 – 6 y – 5 = 0 ANSWERS :
6) 5 x 2 – 20 x – 60 = 0 ANSWERS : -2, 6
7) x 2 + 8 x + 8 = 0 ANSWERS :
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