[the discriminant][section 69]
(1.) x2 + 2x + 8 = 0 here is the problem
b2 - 4ac use the discriminant formula
= (2)2 - 4(1)(8) make substitutions
= 4 - 32 multiply
= -28 subtract
result: there are no real solutions
(2.) 3x2 - 3x - 4 = 0 here is the problem
b2 - 4ac use the discriminant formula
= (-3)2 - 4(3)(-4) make substitutions
= 9 + 48 multiply
= 57 add
result: There are two real solutions
(3.) x2 = 5x + 5 here is the problem
-5x -5x subtract 5x from each side
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x2 - 5x = 5
subtract
-5 -5
subtract 5 from each side
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x2 - 5x - 5 = 0 subtract
b2 - 4ac use the discriminant formula
= (-5)2 - 4(1)(-5) make substitutions
= 25 + 20 multiply
= 45 add
result: there are two real solutions
(4.) 3x2 + 4x - (3/4) =
0 here is the problem
12x2 + 16x - 3 = 0 multiply thru by 4, cancel
b2 - 4ac use
the discriminant formula
= (16)2 - 4(12)(-3) make substitutions
= 256 + 144 multiply
= 400 add
result: There are two real solutions.
(5.) 20x = x2 + 100 here is the problem
x2 + 100 = 20x just rearrange
-20x -20x subtract 20x from each side
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x2 - 20x + 100 = 0 subtract
b2 - 4ac use the discriminant formula
= (-20)2 - 4(1)(100) make substitutions
= 400 - 400 multiply
= 0 subtract
result: There is one real solution.
(6.) 4x2 + 2x - 9 = 0 here is the problem
b2 - 4ac use the discriminant formula
= (2)2 - 4(4)(-9) make substitutions
= 4 + 144 multiply
= 148 add
result: there are two real solutions
(7.) -x2 + 7x - 15 = 0 here is the problem
b2 - 4ac use the discriminant formula
=
(7)2 - 4(-1)(-15)
make substitutions
= 49 - 60 multiply
= -11 subtract
result: there are no real solutions
(8.) (1/2)x2 - 16x + 132 =
0 here is the problem
x2 - 32x + 264 =
0 multiply thru by 2, cancel
b2 - 4ac use the discriminant formula
= (-32)2 - 4(1)(-264) make substitutions
= 1024 + 1056 multiply
= 2080 add
result: there are two real solutions
(9.) x2 - 16 = 0 here is the problem
b2 - 4ac use the discriminant formula
= 02 - 4(1)(-16) make substitutions
= 0 + 64 multiply
= 64 add
result: there are two real solutions
(10.) x2 - 4x + 4 = 0 here is the problem
b2 - 4ac use the discriminant formula
= (-4)2 - 4(1)(4) make substitutions
= 16 - 16 multiply
= 0 subtract
result: there is one real solution