Question

Use the zero product property to find the solutions to the equation 6x^2 – 5x = 56.
x = –8 or x =7/6

x =-8/3 or x =7/2

x =-1/2 or x =56/3

x = -3/7 or x =2/3

Answer 1

Answer:

x = 7/2 or x = -8/3

Step-by-step explanation:

Solve for x over the real numbers:

6 x^2 - 5 x = 56

Divide both sides by 6:

x^2 - (5 x)/6 = 28/3

Add 25/144 to both sides:

x^2 - (5 x)/6 + 25/144 = 1369/144

Write the left hand side as a square:

(x - 5/12)^2 = 1369/144

Take the square root of both sides:

x - 5/12 = 37/12 or x - 5/12 = -37/12

Add 5/12 to both sides:

x = 7/2 or x - 5/12 = -37/12

Add 5/12 to both sides:

Answer:  x = 7/2 or x = -8/3

Answer 2

Step-by-step explanation:

solving for x

6x²-5x=56

subtract 56 from both sides

6x²-5x-56=0

using middle term break method

factorise (56)(6)=(2*2*2*7)(2*3)

=(2*2*2*2) makes 16 and combining(3*7) makes 21

so we have

=6x²+16x-21x-56=0

taking factors out of first two terms and then other two terms

=>2x(3x+8)-7(3x+8)=0

=>(2x-7)(3x+8)=0

either 2x-7=0 or 3x+8=0

2x=7 or 3x=-8

x=7/2 or x=-8/3