x² + 9x - 7 = 0
x² + 9/2x = 7 + (9/2)²
x² + 9/2x = 28/4 + 81/4
(x + 9/2)² = 109/4
x + 9/2 = ± (√109)/2 OR ± 5.2201533
Answer: x = (9 ± √109)/2 OR x = 4.5 ± 5.2201533
We are supposed to complete the square and not find the zeroes of x. (That's porbably the reason why Jun Agruda got 3 TD). Anyway, TU for him.
x² + 9x - 7
= x² + 9x + [(9/2)² - (9/2)²] - 7
Note: (9/2)² - (9/2)² = 0, so the above remains unchanged
= [x² + 9x + (9/2)²] - (9/2)² - 7
= [x + (9/2)]² - (109/4)
If you mean to factor this, it must be the form of an equation.
I'm just guessing here, so I don't know if this is what you're looking for.
For the equation to be a perfect square, what number when doubled, will equal 9?...4.5
4.5 x 4.5 = 20.25
If the equation = -27.25
then
x^2 + 9x - 7 = -27.25
x^2 + 9x + 20.25 = 0
this is a perfect square
(x + 4.5)^2 =0
x would have to be - 4.5
4.5^2 + 9(-4.5) + 20.25 =
20.25 - 40.5 + 20.25 does = 0
x^2 + 9x = 7
x^2 + 9x + 81/4 = 7 + 81/4
(x+9/2)^2 = 28/4 + 81/4
(x+9/2)^2 = 109/4
x+9/2 = (+ or -) Sqrt(109/4)
x = -9/2 (+ or -) Sqrt(109/4)
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Answers & Comments
Verified answer
x² + 9x - 7 = 0
x² + 9/2x = 7 + (9/2)²
x² + 9/2x = 28/4 + 81/4
(x + 9/2)² = 109/4
x + 9/2 = ± (√109)/2 OR ± 5.2201533
Answer: x = (9 ± √109)/2 OR x = 4.5 ± 5.2201533
We are supposed to complete the square and not find the zeroes of x. (That's porbably the reason why Jun Agruda got 3 TD). Anyway, TU for him.
x² + 9x - 7
= x² + 9x + [(9/2)² - (9/2)²] - 7
Note: (9/2)² - (9/2)² = 0, so the above remains unchanged
= [x² + 9x + (9/2)²] - (9/2)² - 7
= [x + (9/2)]² - (109/4)
If you mean to factor this, it must be the form of an equation.
I'm just guessing here, so I don't know if this is what you're looking for.
For the equation to be a perfect square, what number when doubled, will equal 9?...4.5
4.5 x 4.5 = 20.25
If the equation = -27.25
then
x^2 + 9x - 7 = -27.25
x^2 + 9x + 20.25 = 0
this is a perfect square
(x + 4.5)^2 =0
x would have to be - 4.5
4.5^2 + 9(-4.5) + 20.25 =
20.25 - 40.5 + 20.25 does = 0
x^2 + 9x = 7
x^2 + 9x + 81/4 = 7 + 81/4
(x+9/2)^2 = 28/4 + 81/4
(x+9/2)^2 = 109/4
x+9/2 = (+ or -) Sqrt(109/4)
x = -9/2 (+ or -) Sqrt(109/4)