Which of the following rewrites shows the correct process for completing the square?
A- 4x2+9x+5=0 rewritten as 4x2+9x+814=−5+814
B- 3x2−6x−4=0 rewritten as x2−2x+1=4+1
C- 4x2+12x+7=0 rewritten as x2+3x+94=−74+94
D- 2x2−8x−9=0 rewritten as 2x2−8x+16=9+16
A- 4x2+9x+5=0 rewritten as 4x2+9x+814=−5+814
x^2 + 4.5 x = - 5/4 etc, nope
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B- 3x2−6x−4=0 rewritten as x2−2x+1=4+1
x^2 -2 x = 4/3
x^2 - 2 x + 1 = 7/3 nope
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C- 4x2+12x+7=0 rewritten as x2+3x+94=−74+94
x^2 + 3 x = -7/4
x^2 + 3 x + 9/4 = -7/4 + 9/4 I BET YOU HAVE A TYPO AND MEAN THIS
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D- 2x2−8x−9=0 rewritten as 2x2−8x+16=9+16
x^2 - 4 x .... nope
The correct process for completing the square is shown in option D.
In option D, the equation 2x^2 - 8x - 9 = 0 is rewritten as 2x^2 - 8x + 16 = 9 + 16.
To complete the square, you need to add the square of half the coefficient of x to both sides of the equation. In this case, the coefficient of x is -8, so half of it is -4, and the square of -4 is 16.
On the right side of the equation, -9 is replaced with 9 + 16.
This process allows for factoring a perfect square trinomial on the left side of the equation, which is necessary for solving quadratic equations.
The correct process for completing the square involves rearranging the terms of a quadratic equation in order to create a perfect square trinomial. This is done by adding or subtracting a constant term from both sides of the equation. To determine which of the given options is correct, let's go through each one of them.
A- 4x^2 + 9x + 5 = 0 rewritten as 4x^2 + 9x + 814 = −5 + 814
This is not the correct process for completing the square. Adding a constant term to both sides of the equation should result in creating a perfect square trinomial, which is not achieved in this case.
B- 3x^2 − 6x − 4 = 0 rewritten as x^2 − 2x + 1 = 4 + 1
This is not the correct process for completing the square. Similar to option A, we do not obtain a perfect square trinomial by adding a constant term to both sides of the equation.
C- 4x^2 + 12x + 7 = 0 rewritten as x^2 + 3x + 94 = −74 + 94
This is not the correct process for completing the square. Similar to options A and B, adding a constant term to both sides of the equation does not result in a perfect square trinomial.
D- 2x^2 − 8x − 9 = 0 rewritten as 2x^2 − 8x + 16 = 9 + 16
This is the correct process for completing the square. By adding 16 to both sides of the equation, a perfect square trinomial is obtained: (2x - 4)^2 = 25.
Therefore, the correct rewrite that shows the process for completing the square is option D - 2x^2 − 8x − 9 = 0 rewritten as 2x^2 − 8x + 16 = 9 + 16.