Question

Solve (2x + 5)= (2x + 3)(2x - 1)

Answer 1

Answer:

x = -1± sqrt( 33)

    ----------------------------

             4

Step-by-step explanation:

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

Distribute

2x+5 = 4x^2 +6x-2x-3

Combine like terms

2x+5 = 4x^2 +4x -3

Subtract 2x +5 from each side

0 = 4x^2 +4x-3-2x-5

Combine like terms

0 =4x^2 +2x -8

Using the quadratic formula

a=4  b=2  c=-8

x = -b± sqrt( b^2-4ac)

    ----------------------------

             2a

x = -2± sqrt( 2^2-4(4)(-8))

    ----------------------------

             2(4)

x = -2± sqrt( 4+128)

    ----------------------------

             8

x = -2± sqrt( 132)

    ----------------------------

             8

x = -2± 2sqrt( 33)

    ----------------------------

             8

x = -1± sqrt( 33)

    ----------------------------

             4

Answer 2

$(2x + 5)= (2x + 3)(2x - 1)\\2x+5=4x^2-2x+6x-3\\4x^2-2x+6x-3-2x-5=0\\4x^2+2x-8=0\\(4x+1-\sqrt{33})( 4x+1+\sqrt{33})=0 \\ x=\frac{-1+\sqrt{33} }{4} /or/x=\frac{-1-\sqrt{33} }{4}$