2x2 + 14x - 4 = - x2 + 3x

first, lets solve by factoring:

Let's solve your equation step-by-step.

2x2+14x-4=-x2+3x

Step 1: Subtract - x^2+3x from both sides.

2x2+14x-4 - (-x2+3x) = -x2+3x - (-x2+3x)

3x2+11x-4=0

Step 2: Factor left side of equation.

(3x-1) (x+4) = 0

Step 3: Set factors equal to 0.

3x-1=0 or x+4=0

x=

1

3

or x=-4

we can also solve using the quadratic formula:

2x2+14x-4=-x2+3x

Step 1: Subtract - x^2+3x from both sides.

2x2+14x-4 - (-x2+3x) = -x2+3x - (-x2+3x)

3x2+11x-4=0

Step 2: Use quadratic formula with a=3, b=11, c=-4.

x=

-b±√b2-4ac

2a

x=

- (11) ±√ (11) 2-4 (3) (-4)

2 (3)

x=

-11±√169

6

x=

1

3

or x=-4

lastly, we can complete the square.

2x2+14x-4=-x2+3x

Step 1: Add x^2 to both sides.

2x2+14x-4+x2=-x2+3x+x2

3x2+14x-4=3x

Step 2: Subtract 3x from both sides.

3x2+14x-4-3x=3x-3x

3x2+11x-4=0

Step 3: Add 4 to both sides.

3x2+11x-4+4=0+4

3x2+11x=4

Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.

3x2+11x

3

=

4

3

x2+

11

3

x=

4

3

Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.

Then we need to add (b/2) ^2=121/36 to both sides to complete the square.

Add 121/36 to both sides.

x2+

11

3

x+

121

36

=

4

3

+

121

36

x2+

11

3

x+

121

36

=

169

36

Step 6: Factor left side.

(x+

11

6

) 2=

169

36

Step 7: Take square root.

x+

11

6

=±√

169

36

Step 8: Add (-11) / 6 to both sides.

x+

11

6

+

-11

6

=

-11

6

±√

169

36

x=

-11

6

±√

169

36

x=

1

3

or x=-4

Answer:

x=

1

3

or x=-4