(5×100)+(6×110)+(7×1100) What is this number in standard form?
2 answers:
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That trinomial can't be factored. You would have to complete the square to factor it and even then your answer would be an imaginary number.
x² + x + 12 = 0
x² + x = - 12
x² + x + 1/4 = - 12 + 1/4
x² + x + 1/4 = - 11 3/4
x² + x + 1/4 = - 47/4
(x + 1/2)² = - 47/4
x + 1/2 = +/- √(- 47/4)
x + 1/2 = +/-
x = 1/2 +/-
If the constant was a negative, it would be factor-able (is that a word?).
x² + x + 12 = 0
x² + x = - 12
x² + x + 1/4 = - 12 + 1/4
x² + x + 1/4 = - 11 3/4
x² + x + 1/4 = - 47/4
(x + 1/2)² = - 47/4
x + 1/2 = +/- √(- 47/4)
x + 1/2 = +/-
x = 1/2 +/-
If the constant was a negative, it would be factor-able (is that a word?).
Answer:
Step-by-step explanation:
We have the sides for both the rectangle and the square. The problem says that the area of the rectangle is 16 more than the area of the square. The area of the rectangle is
(x + 16)(x)
The area of the square is
(3x - 2)(3x - 2)
"The area of the rectangle" "is" "16 more than the area of the square"
x(x + 16) = (3x - 2)(3x - 2) + 16
FOILing the left side and then setting it equal to the FOILing of the right side:
and
Now we will get everything on the same side of the equals sign, set the polynomial equal to 0, and factor to solve for x:
Factor that however you learned best to factor quadratics (the quadratic formula works for a second degree polynomial every time!) to get that
x = 1 or x = 2.5