Mathematics, 19.07.2019 06:30 michellemunoz250

How do you solve basic quadratic equations, using the "completing the square" method. i know how to use the quadratic formula but don't know how to solve by completing the square.

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Answer from: bbygrill

So, we have 80 = x² -16x.

first off, we start by grouping the terms with "x".

80 = (x² - 16x)

80 = (x² - 16x + [?]²) <--- we have a missing fellow.

so, the idea being, we need "some value" to get our perfect square trinomial, hmmm what could that be?

well, the tell-tale guy is the middle term, we know that 2(√ guy on the left)(√ guy on the right) is the middle term.

we know the square root of the (√x²) is just "x", and the guy on the right is [?], but we also know that if we multiply 2 times both we get 16x, so

$\bf 2(x)\left(\boxed{?}\right)=16x\implies \boxed{?}=\cfrac{16x}{2x}\implies \boxed{?}=8$

aha! there's our missing fellow, so we need to add 8².

however, bear in mind, all we're doing is borrowing from our very good friend Mr Zero, 0.

so if we add 8², we also have to subtract 8².

$\bf 80=(x^2-16x+8^2-8^2)\implies 80=(x^2-16x+8^2)-64
\\\\\\
144=(x^2-16x+64)\implies 144=(x-8)^2\implies \pm\sqrt{144}=x-8
\\\\\\
\pm 12 = x-8\implies \pm 12 + 8 = x\implies x=
\begin{cases}
20\\
-4
\end{cases}$

Answer from: Quest

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.

Answer from: Quest

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = $\frac{-8+3}{4-7}$ = - $\frac{5}{3}$

y = - $\frac{5}{3}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - $\frac{20}{3}$ + c ⇒ c = - $\frac{4}{3}$

y = - $\frac{5}{3}$ x - $\frac{4}{3}$ ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

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