Solve each equation by completing the square

1. y² - 2y = 15

2. x² - x - 5/3 = 0

3. 4x² + 12x - 7 = 0

4. The time t in seconds for a car to skid 12 feet is given by
12 = -12t + 9t²
Use any method to solve for t. (Choose the answer that is reasonable for this situation.)

1(y^2 -2y) = 15

1(y^2 -2y +1^2 -1^2) = 15

1(y^2 -2y +1) +1(-1) = 15

1(y-1)(y-1) = 15 + 1

(y-1)^2 = 16

y - 1 = +/- √16 <---ne number positive or negative squared ends up positive!

y = 1 +/- 4

y1 = 1 - 4

y1 = -3

y2 = 1 + 4

y2 = 5

THEREFORE y= -3, 5








x^2 - x = 5/3

1(x^2 -x) = 5/3

1(x^2 -x +1/2^2 - 1/2^2) = 5/3

1(x^2 -x +1/4) +1(-1/4) = 5/3

1(x^2 -x +1/4) -1/4 = 5/3

1(x -1/2)(x -1/2) = 20/12 + 3/12

(x - 1/2)^2 = 23/12

square root both sides

x - 1/2 = +/- √(23/12)

x = 1/2 +/- √(23/12)

simplify.

x = 1/2 +/- (√23)/2√3

rationalize denominator

x = 1/2 +/- (√23)(2√3) / 2√3(2√3)

x = 1/2 +/- (2√66)/4(3)

x = 1/2 +/- 2√66/12

x = 1/2 +/- 2√66 / 12

x = 1/2 +/- 1√66 / 6

x = 3/6 +/- √66/6

x = (3 +/- √66) /6

can't simplify further.









4x^2 +12x = 7

4(x^2 +3x) = 7

4(x^2 +3x +3/2^2 - 3/2^2) = 7

4(x^2 +3x +9/4) +4(-9/4) = 7

4(x +3/2)(x +3/2) -9 = 7

4(x +3/2)^2 = 7 + 9

4(x +3/2)^2 = 16

(x +3/2)^2 = 16/4

x + 3/2 = +/- √4

x = -3/2 +/- 2

x1 = -3/2 - 4/2

x1 = -7/2

x2 = -3/2 + 4/2

x2 = 1/2

THEREFORE x= -7/2, 1/2