Question

Guys, I beg you! How do you do these factoring quadratic equations!

Which is a solution to (x − 2)(x + 10) = 13

Answer 1

times the x’a together and x*10 then 2*x and 2*10

Answer 2

Answers: x = -11 and x = 3

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Step-by-step explanation:

There are at least three ways to solve this.

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Method 1:

We could graph y = (x-2)(x+10) using a tool like Desmos. Graph y = 13 as well which is a horizontal line.

Check out the screenshot shown below.

The parabola in red and the horizontal line in blue intersect at the locations (-11, 13) and (3, 13)

We only focus on the x coordinates of the intersection points.

Therefore, the two solutions are x = -11 and x = 3

The order of the solutions doesn't matter.

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Method 2:

Expand things out and get everything to one side

(x-2)(x+10) = 13

x^2 + 10x - 2x - 20 = 13

x^2 + 8x - 20 - 13 = 0

x^2 + 8x - 33 = 0

From here we can use the quadratic formula

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-8\pm√((8)^2-4(1)(-33)))/(2(1))\\\\x = (-8\pm√(64+132))/(2)\\\\x = (-8\pm√(196))/(2)\\\\x = (-8\pm14)/(2)\\\\x = (-8+14)/(2) \ \text{ or } \ x = (-8-14)/(2)\\\\x = (6)/(2) \ \text{ or } \ x = (-22)/(2)\\\\x = 3 \ \text{ or } \ x = -11\\\\`

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Method 3:

Instead of using the quadratic formula, we could factor.

To factor x^2+8x-33, we need to find two numbers that

• Multiply to -33
• Add to 8

Through trial and error, you should get 11 and -3

• 11 times -3 = -33
• 11 plus -3 = 8

So,

x^2+8x-33 = 0

(x+11)(x-3) = 0

x+11 = 0 or x-3 = 0

x = -11 or x = 3