Question

Solve each of the following equations for x using the Quadratic Formula. Round your answer to two decimal places, if necessary.SHOW ALL WORK
1. Solve x2 + 3x – 4 = 0
2. Solve 2x2 – 4x – 3 = 0
3. Solve x(x – 2) = 4
4. Solve 9x2 + 12x + 4 = 0
5.Solve x2 + 2x = 1

Answer 1

x^2 + 3x -4 = 0

x= -3 +-√( 9 -4(-4))/ 2

= -3 +-√(9 +16) ))/2

= -3+-√25))/2

= -3+-5)/2

= -3+5)/2, -3 -5)/2

= 2/2, -8/2

= 1,-4

2)2 x^2 -4x-3= 0

x= 4+-√(16 -4(2)(-3))/ 2(2)

= 4+- √(16 + 24))/ 4

= 4+-√40)/ 4

= 4+-2√10)/4

= 1+ √10/2, 1- √10/2

= 1+ 3.16/2, 1- 3.16/2

= 1+1.58, 1- 1.58

= 2.58,-0.58

3)x( x-2) = 4

x^2 - 2x -4 = 0

x= 2+-√4-4(-4))/ 2

= 2+-√4+16)/ 2

= 2+-√20)/2

= 2+-2√5)/2

= 1+-√5

= 1+√5, 1-√5

= 1+2.23, 1-2.23

= 3.23, -1.23

4)9 x^2 +12 x +4 = 0

x= -12 +-√144 - 4(9)(4)))/2(9)

= -12 +-√144- 144))/18

= -12/18 = -2/3 = -0.66

5)x^2 +2x = 1

x^2 +2x -1= 0

x= -2+-√4-4(-1))/ 2

= -2+-√4+4))/2

= -2+-√8)/2

= -2+-2√2)/2

= -1 +-√2

= -1+√2, -1-√2

= -1+1.41, -1-1.41

= 0.41, -2.41