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Using the quadratic formula:

a = 2, b = 6, c = 5

x = (-b plusminus sqrt(b2 - 4ac))/2a

x = (-6 plusminus sqrt(36 - 40))/4

x = (-6 plusminus sqrt(-4))/4

As you can see, this has resulted in the square root of a negative number, which is not usually possible. You may not need to know about imaginary numbers yet, but the solution to this can actually be given using the imaginary constant, i, with the answer being a complex number (a real number combined with an imaginary number).

x = (-6 plusminus 2i)/4

x = -3/2 + i/2 and -3/2 - i/2

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That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: (-5 plus or minus the square root of 3) divided by 2

x = -1.6339745962155614

x = -3.3660254037844384

2x2 - 5x - 3 = 0

This equation can be factored :

(2x + 1)(x - 3) = 0

It can't be factored because its discriminant is less than zero

3x2-x-2

(3x+2)(x-1)

(x+3)(x-8) = 0

(x + 5)(2x - 1)

7

Q: How do you factor 2x2 plus 10x plus 11 equals 0?

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The factorisation is as follows: 2x2 + 7x - 9 = (x - 1)(2x + 9).

6ab(2x2+x-5)

If that's - 338, the answer is 2(x + 13)(x - 13)

2x2+10x+12/(x+3)We use long division just like we would normally.Let me give you an example.ex:Divide 7 into 23---------7 | 234We say ok, how many times does 7 go into 2?0 times, it doesn't work. So you put a 0 above the 2.Now we try 7 into 23. It can go 3 times, so we put a 3 above the 3 (in 234) and subtract 21. (3 *7) and then carry down the 4....03--------7|234-..21--------...024how many times will 7 go into 24? 3 again....033-------7|234-..21-------...024-....21--------.......3We're left with 3 as the remainder.Our answer to 234 divided by 7 is 33 remainder of 3, or 33 and 3/7.----This method works similarly with variables.2x2+10x+12/(x+3)----------------------x+3|2x2+10x+12We'll start the same way. How many times will X go into 2x2Or, what times X gives 2x2 x * 2x = 2x2So we write a 2x above the 2x2, just like we wrote the 3 in the example above........2x----------------------x+3|2x2+10x+12Now we multiply x+3 by 2x to figure out what to subtract.2x(x+3)= 2x2 +6xNotice we ended up with a 2x2? This is what we wanted to subtract! Something to note, when you do your subtraction, you're subtracting the entire expression 2x2 +6x.So you can write -2x2 - 6x........2x----------------------x+3|2x2+10x+12......-2x2 - 6x-----------------...............4x + 12Make sure you carry down the next term, the +12. Just like we carried down the 4 in the example above.Now, how many times will X go into 4x? 4 times. So we write a 4 next to the 2x.and then multiply 4(x+3). then subtract........2x + 4----------------------x+3|2x2+10x+12......-2x2 - 6x-----------------...............4x + 12..............-4x - 12---------------------........................0In this scenario we get a remainder of 0.This means that x+3 divides evenly into 2x2+10x+12.In fact, it can divide into it 2x +4 times.To check this, multiply (x+3)(2x+4) use FOIL.(x+3)(2x+4) = 2x2+10x+12 (check)Side note: If you did get a remainder, like in the 1st example. Let's say the remainder was 1.You take the remainder, 1 and put it over the divisor x +3.so your answer would be 2x+4 +(1/x+3)

y=2x2+5. Plug in 0 for x, and you get y=2(0)^2 +5 =0+5=5. 5 is the minimum value for y.

Related questions

Doesn't factor evenly, use quadratic

2x2 + 10x + 25 is a quadratic expression. It describes a parabola.

The roots of the equation are [5 +/- sqrt(11)]/2 = 4.158 and 0.842

20x3 - 70x2 + 60x = 10x(2x2 - 7x + 6) = 10x(2x - 3)(x - 2).

2x2 = 10x + 12 2x2 - 10x - 12 = 0 x2 -5x -6 = 0 x2 - 6x + x - 6 = 0 x(x -6) + 1(x -6) = 0 (x+1)(x-6) = 0 x = -1 or x = 6

2(x + 3)(x + 2)

2x2 equals 5

6x3 - x2 + 17 = 2x2 + 47 6x3 - x2 - 2x2 = 47 - 17 x2(6x - 1 - 2) = 30 this is the simplest factorisation.

(-5 plus or minus the square root of 11) divided by 2 x = -0.8416876048223001 x = -4.1583123951777

3

2x2 + 7x - 15 = 02x2 + 10x - 3x - 15 = 0(2x2 - 3x) + (10x - 15) = 0x(2x - 3) + 5(2x - 3) = 0(2x - 3)(x + 5) = 0(2x - 3) = 0 or (x + 5) = 0x = 3/2 or x = -5

2x2 + 10 - 9x = 0 or 2x2 - 9x + 10 = 0 So (x - 2)*(2x - 5) = 0