ax² + bx + c = 0
x = (-b ± √(b² - 4ac))/2a
First, rewrite the first equation so that the first coefficient is 1. Divide everything by a.
(ax² + bx + c = 0)/a =
x² + (b/a)x + (c/a) = 0
Isolate (c/a) by subtracting (c/a) from both sides
x² + (b/a)x + (c/a) (-(c/a) = 0 (- (c/a)
x² + (b/a)x = 0 - (c/a)
Add spaces
x² + (b/a)x = -c/a
Take 1/2 of the middle term's coefficient and square it. Remember that what you add to one side, you add to the other.
x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²
Simplify the left side of the equation.
x² + (b/a)x + (b/2a)² = (x + (b/2a))²
(x + b/2a))² = ((b²/4a²) - (4ac/4a²)) -> ((b² - 4ac)/(4a²))
Take the square root of both sides of the equation
√(x + b/2a))² = √((b²/4a²) - (4ac/4a²))
x + b/(2a) = (±√(b² - 4ac)/2a
Simplify. Isolate the x.
x = -(b/2a) ± (∛b² - 4ac)/2a = (-b ± √(b² - 4ac))/2a
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Answer:
y= 1/4x + 1
Step-by-step explanation:
Answer:
A) 50
B) 20
C) 20
Step-by-step explanation:
To solve the first question, we can multiply both sides by 10.
Thus, we get:
6x = 300.
Then, divide by 6, to get x:
x = 50.
You can do the same thing to all of these questions.
I've already checked the answers, but if you don't trust them, just pluck the values in.
For example, let's check the answer for question A.
0.6*50 is supposed to equal 30.
Does it equal? Yes, so we know that the answer is correct.
Answer:
(8,5)
Step-by-step explanation:
5x - 2y = 30
coordinates are (x,y) so you plug in 8 for x and solve for y
5(8) - 2y = 30
40 - 2y = 30
subtract 40 from both sides to isolate y
-2y = -10
divide both sides by -2 to isolate y
y = 5
