1. Solve for x, and check.

 

2x^2+3x=20

This is a quadratic equation so we run through the steps for solving quadratic equations.

 

Transpose all terms to one side leaving a zero on the other.

 

2x^2+3x-20=0

 

Factor

 

(2x-5)(x+4)=0

 

Set the factors = 0, and solve the resulting equations.

 

2x-5=0,2x=5,x=5/2;x+4=0,x=-4

 

check

Let x = 5/2. Then the equation becomes

 

2(5/2)^2+3(5/2)=20

 

Do the power first

2(25/4)+3(5/2)=20

 

 

Next multiply

 

25/2+15/2=20

 

Add the fractions on the left. Note that we have common denominators.

 

40/2=20

 

which checks.

 

Next let x = -4. The equation becomes

 

2(-4)^2+3(-4)=20

 

Do the power first.

 

2(16)+3(-4)=20

 

Then multiply.

 

32-12=20

 

which checks.

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