Mathematics, 06.02.2020 02:50 emilyrocks618

How do you do the last question using the quadratic formula?

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Answer from: emmat1220

x = -1

Step-by-step explanation:

To do the last question using the quadratic formula, you first need the equation in standard form.

ax² + bx + c = 0.

To convert 2(x - 2)(x + 1) = x² - 4x - 5 into standard form, simplify by expanding and collecting like terms. Then, have the equation equate to "0" by moving everything to one side.

2(x - 2)(x + 1) = x² - 4x - 5 Expand brackets first using FOIL

2(x² + x - 2x - 2) = x² - 4x - 5 Collect like terms in brackets (x - 2x = -x)

2(x² - x - 2) = x² - 4x - 5 Distribute, multiply bracket numbers by "2"

2x² - 2x - 4 = x² - 4x - 5 Now make the equation equal 0

2x² - 2x - 4 - x² = x² - 4x - 5 - x² Subtract x² from both sides

x² - 2x - 4 = -4x - 5 "x²" eliminated from the right side. Simplify left side.

x² - 2x - 4 + 4x = -4x - 5 + 4x Add 4x to both sides.

x² + 2x - 4 = -5 "4x" eliminated from right side. Simplify left side.

x² + 2x - 4 + 5 = -5 + 5 Add 5 to both sides to eliminate it on the right.

x² + 2x + 1 = 0 Simplified left side.

This is now in standard form. State the "a", "b" and "c" values based on the standard form variables.

a = 1; b = 2; c = 1

Substitute into the quadratic formula

$x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}$ (Please ignore the Â, it's a formatting error)

$x = \frac{-2±\sqrt{2^{2}-4(1)(1)} }{2(1)}$ Simplify the square root

$x = \frac{-2±\sqrt{0} }{2}$ The square root of 0 is 0.

$x = \frac{-2}{2}$ The numerator can only be -2. Simplify the fraction

x = -1 Only one answer for "x".

Whenever the square root equals "0", there will only be one answer for "x".

Answer from: Quest

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

Answer from: Quest

lol 2

step-by-step explanation:

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