SOLUTION: Use the quadratic formula to solve each of the following quadratic equations... 1. 2x^2-5x=3 2. 3x^2-2x+1=0 3. x^2+4x+4=7 (Hint: Factor the left hand side)

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Question 85397: Use the quadratic formula to solve each of the following quadratic equations...
1. 2x^2-5x=3
2. 3x^2-2x+1=0
3. x^2+4x+4=7 (Hint: Factor the left hand side)
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
1.

Subtract 3 from both sides
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=49 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -0.5. Here's your graph:


2.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -8 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -8 is + or - .

The solution is

Here's your graph:



3.

Subtract 7 from both sides
Combine like terms
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=28 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.645751311064591, -4.64575131106459. Here's your graph:
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