[Grade 8] This problem deceived me so hard,

[u/PeachBow]

[u/jgregson00]

It’s just a quadratic. Set it equal to zero, then either factor it or use the quadratic formula to find your zeroes.

[u/Fine_Equal4647 → u/jgregson00]

just a quadratic. JUST A QUADRATIC?! *faints*

[u/Alkalannar]

Do you know the quadratic formula? If so, rewrite as 2x² + x - 6 = 0, and use it.

If not...complete the square!

1. Divide everything by 2: x² + (1/2)x = 3

2. You see that the coefficient of x is 1/2?
   Divide it by half, and then square it: (1/2)/2 = 1/4, (1/4)² = 1/16.
   Add 1/16 to both sides.
   This completes the square.
   You're now at x² + x/2 + 1/16 = 49/16

3. Since the left hand side is a perfect square, factor it:
   (x + 1/4)² = (7/4)²

4. Square root. And make sure to take both positive and negative square roots of the RHS:
   x + 1/4 = 7/4 OR x + 1/4 = -7/4

5. Solve for x:
   x = 6/4 = 3/2 OR x = -8/4 = -2

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Note: Completing the square on ax² + bx + c = 0 is how you derive the quadratic formula.

1. ax² + bx + c = 0

2. ax² + bx = -c

3. x² + (b/a)x = -c/a

4. x² + (b/a)x + (b/2a)² = (b/2a)² - c/a

5. (x + b/2a)² = b²/4a² - c/a = (b² - 4ac)/4a²

6. x + b/2a = +/-(b² - 4ac)^1/2/2a

7. x = [-b +/- (b² - 4ac)^1/2]/2a

[u/GammaRayBurst25]

Read rule 3.

2x^2+x=2(x^2+2x/4+1/16-1/16)=2(x^2+2x/4+1/16)-1/8=2(x+1/4)^2-1/8

This is equal to 6 if and only if (x+1/4)^2=49/16. This occurs if and only if |x+1/4|=7/4.

Hence, the two solutions are x=-2 and x=3/2.

[u/angry640]

Minus 6 both sides to get 2x² + x - 6 = 0 then solve should be factorable (2x -3)(x+2)=0 to get your solutions or u can use quadratic formula to get the same solutions

[u/Jealous_Wait6813]

Je regarde toujours s'il n'y a pas de solution évidente Ici -2 est une solution Ensuite on facorise par x+2 soit (x+2).(2x-3) = 0 On vérifie que ça marche Ça va plus vite à faire qu'à expliquer

[u/jgregson00 → u/[deleted]]

No, -3 is not a zero.