you basically could enter some values into your equation to get your data. x^2 - 3x + 6 > 0 At x = a million and x = 2 you get +4. x=a million: a million - 3 + 6 = -2 + 6 = 4 x=2: 4 - 6 + 6 = -2 + 6 = 4 it quite is the backside attainable fee. on each occasion x = a detrimental quantity, your first term x^2 is helpful, your 2nd term (-3x) is helpful, and +6 is often helpful. while x = 3, your first and 2nd words cancel: 9 - 9 + 6, leaving +6. For all values extra suitable than 3, your x^2 term gets larger and bigger and the version between x^2 and 3x additionally gets larger and bigger. as an occasion, x = 4 yields sixteen - 12 (+6), x = 5 yields 25 - 15 (+6), x = 6 yields 36 - 18 (+6); the transformations 4, 10, 18 get steadily extra suitable. At x = 10, x^2 = one hundred, 3x = 30 x^2 -3x = one hundred - 30 (+6). This equation is helpful for all values of x. actual.
Answers & Comments
Verified answer
False
It is x^2 +6x +9
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you basically could enter some values into your equation to get your data. x^2 - 3x + 6 > 0 At x = a million and x = 2 you get +4. x=a million: a million - 3 + 6 = -2 + 6 = 4 x=2: 4 - 6 + 6 = -2 + 6 = 4 it quite is the backside attainable fee. on each occasion x = a detrimental quantity, your first term x^2 is helpful, your 2nd term (-3x) is helpful, and +6 is often helpful. while x = 3, your first and 2nd words cancel: 9 - 9 + 6, leaving +6. For all values extra suitable than 3, your x^2 term gets larger and bigger and the version between x^2 and 3x additionally gets larger and bigger. as an occasion, x = 4 yields sixteen - 12 (+6), x = 5 yields 25 - 15 (+6), x = 6 yields 36 - 18 (+6); the transformations 4, 10, 18 get steadily extra suitable. At x = 10, x^2 = one hundred, 3x = 30 x^2 -3x = one hundred - 30 (+6). This equation is helpful for all values of x. actual.
(x+3)(x+3) = x2 +9
multiply out the brakets: x squared + 6x + 9= x2+9
x squared +6x +9 does not equal x2 +9
so it is false. :)
p.s oh if you mean x2 is x squared the answer is stil false because:
x squared + 6x +9 still doesn't equal x squared +9 (x squared + 9 doesn't have a 6x in the equation.
it's false, (x+3)(x+3) = x2 + 6x + 9
Simplifying
(x + 3)(x + 3) = x2 + 9
Reorder the terms:
(3 + x)(x + 3) = x2 + 9
Reorder the terms:
(3 + x)(3 + x) = x2 + 9
Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) = x2 + 9
((3 * 3 + x * 3) + x(3 + x)) = x2 + 9
((9 + 3x) + x(3 + x)) = x2 + 9
(9 + 3x + (3 * x + x * x)) = x2 + 9
(9 + 3x + (3x + x2)) = x2 + 9
Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) = x2 + 9
Reorder the terms:
9 + 6x + x2 = 9 + x2
Add '-9' to each side of the equation.
9 + 6x + -9 + x2 = 9 + -9 + x2
Reorder the terms:
9 + -9 + 6x + x2 = 9 + -9 + x2
Combine like terms: 9 + -9 = 0
0 + 6x + x2 = 9 + -9 + x2
6x + x2 = 9 + -9 + x2
Combine like terms: 9 + -9 = 0
6x + x2 = 0 + x2
6x + x2 = x2
Add '-1x2' to each side of the equation.
6x + x2 + -1x2 = x2 + -1x2
Combine like terms: x2 + -1x2 = 0
6x + 0 = x2 + -1x2
6x = x2 + -1x2
Combine like terms: x2 + -1x2 = 0
6x = 0
Solving
6x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '6'.
x = 0
Simplifying
x = 0
false.
(x+3)(x+3) = x2+6x+9
(x + 3)(x + 3)
= x(x) + x(3) + 3(x) + 3(3)
= x^2 + 3x + 3x + 9
= x^2 + 6x + 9
x^2 + 6x + 9 ≠ x^2 + 9
But...
If x = 0, x^2 + 6x + 9 = 9 and x^2 + 9 = 9, they are equal.
∴ (x + 3)(x + 3) ≠ x^2 + 9 (if x ≠ 0)
FALSE
(x+3)(x+3) = (x+3)^2
x^2+9 = x^2+3^2 this is different from (x+3)^2
False. it's actually x^2 + 6x + 9.
You have an equation.
There are two kinds of equations:
1. Identities (they are to be true unconditionally; that is, for all values of 'x').
2. Non-identities (they are true only conditionally: for certain value(s) of 'x').
If your equation is supposed to be an identity, then the answer is "False". If it isn't an identity, the answer is "True only if x = 0."