If four times a whole number is subtracted from three times the square of the number, the result 15 is obtained. Find the number.
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What you need is to learn how to do these
types of problems.
"4 times a whole number" ... 4x
"is subtracted from three times the
square of the number" ... 3x2 - 4x
"the result 15 is obtained"
3x2 - 4x = 15
Subtract 15 from both sides
3x2 - 4x - 15 = 0
This can be factored by grouping. Multiply
the coefficient of x2 by the constant:
3(-15) = -45
Look for factors of -45 that add to -4:
-9(5)=-45 ... -9+5 = -4
Replace -4x with -9x+5x and factor by grouping
3x2-9x +5x - 15 = 0
(3x2-9x) + (5x-15) = 0
3x(x-3) + 5(x-3) = 0
(3x+5)(x-3) = 0
Your two answers are found by realizing that
this is true if either
3x+5 = 0 or (x-3) =0
Solve these two simple equations to get the
final two values of x
Step-by-step explanation:
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