You should know the BEST way to solve this quadratic equation

How to solve a quadratic equation.

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TC Math Notes

[leetrask]

Add 3 to each side of the equation. Take square root of both sides. x+2 = + or - 5.

[MFisher]

When I first learned about the quadratic formula (about 60 years ago) I was taught that b^2 - 4ac was known as 'the determinant' and if it was equal to zero there would be only one solution (or two identical solutions if you want to split hairs).

[vcut]

I used the quadratic formula and I love it 😍
Thanks for posting, you run my favorite YouTube channel, along with Mentour Pilot and Mark Felton.

[nickcellino]

The fifth method, not given, is the Sums and Products Method which is often the fastest and easiest method to solve quadratic equations.

(x+2)(x+2) -3 = 22

Step 1: Simplify into a quadratic equation: x² + 4x -21 = 0

Step 2: Determine the sum of the roots and the product of the roots. The sum of the roots is always the coefficient for x with the sign reversed. Here this is -4. The product of the roots is always the constant which here is -21.

Step 3: Ask what two numbers are -21 when multiplied and -4 when added.

Since the product of the roots is negative, there must be one positive root and one negative root. Since the sum of the roots is negative, the absolute value of the negative root must be larger than the positive root. Now it's easy to determine that the roots are -7 and +3.

Sometimes quickly determining the roots from the sum and product of the roots is very difficult so this method can't always be relied upon to find the roots easily but because it's so fast and easy, it should be the first method tried.

P.S. If it's a multiple choice question, it's even easier to solve. Among the 5 choices, determine which choice has roots equal to -21 when multiplied. If there are no duplicates, that's the right choice. If there's a duplicate, perform the sum calculation among the duplicates to find the right answer.

[jamesmccamish]

Outstanding lesson, touches on so many aspects of Q equations.

[nuffroom]

Solved for x = 3 in my head in seconds. Good job, keep up the fun questions! 👍👍👍

[panlomito]

x² + 4x + 4 - 3 - 21 = x² + 4x -21 = 0 -> ( x+7 ) . ( x - 3 ) = 0 -> x1 = -7 and x2 = 3

With abc-formula:
discriminant: D = b² - 4ac = (4)² - 4 . (1) . (-21) = 16 + 84 = 100
x-coordinate of the top: xtop = -b / 2a = -(4) / 2.1 = -2 and
because of symmetry: xtop = ( x1 + x2 ) / 2 = ( -7 + 3 ) = -2
y-coordinate of top: ytop = (-2)² + 4(-2) - 21 = 4 - 8 - 21 = - 25
distance between xtop and x1, x2: delta = SQR(D) /2a = 10/2 = 5

x1 = xtop - delta = -2 - 5 = -7
x2 = xtop + delta = -2 + 5 = 3

[ange-bernardferracci]

Very Google explanatio ❤❤❤ best regards to xplus 2 and to 22 and 3 which are good fellows also❤❤❤❤

[danieldennis]

It would be an easy mistake to just add 3 to both sides and just take the square root of both sides. But Pemdas says multiply first. So x=3 or -7.

[stevenjohnson]

X is 3 or -8 since we need either 5 or -5 twice in this quadratic

[harrymatabal]

x=3 or -7, that s my method mentally. Can you beatthat

[riedki]

Why don't you apply + and - minus the left hand, that is + and - (x+2)

[BansheeBunny]

I added 3 to 22 then looked at the rest of the problem and it screamed the answer at me.

[hhgygy]

This is overcomplicated, you don't need the quadratic formula at all if you simply replace x+2 with y and rewrite the equation as y²-3=22 => y²=25 => y₁=5;y₂=-5=>x₁=3;x₂=-7

[aryusure]

Yeah! That tricky question again with its 2 solutions when one suffices. ;)
I got 3 in 10 seconds in my head and got fooled by the quadratic stuff again.

[olenfersoi]

I thought you said that, when solving an equation gives positive and negative answers, the positive answer is considered the correct one? While -7 would be the quadratic equation's second answer, 99% of persons would not answer +/-5 as the square root of 25. And, a calculator will answer "5"...not positive or negative!

[ange-bernardferracci]

Le 22 passe et vote à gauche associé au 3 il devient un 25 négatif .. à eux deux pour jouer le rôle du carré de 5 ils sont parfaits L union fait la force. X+2 multiplié par lui même devient aussi un carré par principe du miroir. On peut former a2-b2 qui devient (a-b)(a+b) ..pour affirmer que l equipe multipliée est nulle connaît la suite ...

[Postmortumaz]

That's a quadraradicle equation thing. Because there a bunch of letters and numbers.

[jeswantharaopasupuleti]

So again, we're not using a calculator. Now what happens when you don't have your calculator.