SOLUTION: Could you help solve the quadratic equatin by completing the square 2x^2

SOLUTION: Could you help solve the quadratic equatin by completing the square 2x^2 - 6x + 5 Thank You, Stacie Rihl

Question 260559: Could you help solve the quadratic equatin by completing the square
2x^2 - 6x + 5
Thank You,
Stacie Rihl
Found 2 solutions by onlinetutor365.com, jim_thompson5910:
Answer by onlinetutor365.com(14) (Show Source): You can put this solution on YOUR website!

2(x2) - 6x + 5 = 0
Solving for variable 'x'.
Begin completing the square. Divide all terms by 2 the coefficient of the squared term:
Divide each side by '2'.
x^2 - 3x + 2.5 = 0
Move the constant term to the right:
Add '-2.5' to each side of the equation.
x^2-3x +2.5 -2.5=-2.5
x^2 -3x =-2.5

The x term is -3x. Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.
Add '2.25' to each side of the equation.
x2-3x + 2.25 = -2.5 + 2.25

x2-3x + 2.25= -0.25
Factor a perfect square on the left side:
(x -1.5)(x -1.5) = -0.25
Can't calculate square root of the right side.
The solution to this equation could not be determined.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So .

So is equivalent to .

Now let's solve

Start with the given equation.

Subtract from both sides.

Combine like terms.

Divide both sides by .

Reduce.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Take the square root of to get .

Note:

or Add to both sides.

--------------------------------------

Answer:

So the solutions are or .

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