Solve the equation 4x^2-4x-1=0
1 answer:
Answer:
x = (1 ±√2)/2
Step-by-step explanation:
We can "complete the square" to solve this.
4x^2 -4x = 1 . . . . add 1
x^2 -x = 1/4 . . . . .divide by 4 to make x^2 coefficient = 1
x^2 -x +1/4 = 2/4 . . . . add the square of half the x-coefficient: (-1/2)^2 = 1/4
(x -1/2)^2 = 2/4 . . . . write as a square
x -1/2 = ±(√2)/2 . . . . . take the square root
x = (1 ±√2)/2 ≈ {-0.2071, 1.2071}
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Answer:
Step-by-step explanation:
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Answer:
d) one solution; (4, 1)
Step-by-step explanation:
It often works well to follow problem directions. A graph is attached, showing the one solution to be (4, 1).
_____
You know there will be one solution because the lines have different slopes. Each is in the form ...
y = mx + b
where m is the slope and b is the y-intercept.
The first line has slope -1 and y-intercept +5; the second line has slope 1 and y-intercept -3. The slope is the number of units of "rise" for each unit of "run", so it can be convenient to graph these by starting at the y-intercept and plotting points with those rise and run from the point you know.
