Solving Quadratic Equations by Factoring Solve the following...

Solving Quadratic Equations by Factoring Solve the following quadratic equations by factoring. First write the equations in completely factored form. Then write the real number solutions. [Hint: Remember to use proper notation when writing the real number solutions. For example: if the solutions are $x = 1$ and $x = 4$, write $x = 1, 4$ $x^2 + 15x + 56 = 0$ $x^2 - x - 72 = 0$ Factored Form Factored Form Real Number Solutions Real Number Solutions

Transcript

00:07 The first equation that we have is x squared plus 11x equals to negative 30.

00:15 Or you can write down and it in this manner, x square plus 11x plus 30 equals to 0.

00:23 Now, you need to split this middle term.

00:25 In order to factorize it, you need to split this middle term such that their product will be equal to 1 into 30.

00:32 So you can break this number 11x into 6x plus 5x.

00:38 Now, what is the magic over here? 6x into 5x, that gives you 30.

00:43 All right.

00:44 Okay.

00:45 So, this is the first factorized form.

00:47 You can take out x common, you will get x plus 6, you can take out 5 common, you will get x plus 6, all right.

00:54 And from both the brackets, you can take out x plus 6 common.

00:58 You'll get x plus 6 times x plus 5 as your factorized form.

01:04 Okay.

01:04 And when you're going to solve this, you will get x is equals to negative 6.

01:08 And negative 5 as the two real solutions, okay? this is the very first solution.

01:14 Let's talk about another one which is x squared minus 20 equals to x.

01:19 So i'll just write it down over here with the right color.

01:23 So x squared minus 20 equals to x.

01:32 Again, you can just write it down into the standard format that's x squared minus 6 minus 20 equals to 0.

01:39 Again, now how you're going to factorize this? x squared minus 5x plus 4x minus 20 equals to 0.

01:47 Now why i did so? because minus 5 times 4 is going to give you minus 20.

01:52 All right...

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