# Twice the square of a number is 16 less than 10 times the number. Find the number

1
by nickahcabiao
I'm almost brain-dead thinking for the answer in this question.
I'm thinking of using quadratic formula for this. it can be write as 2x^2 - 10x + 16 = 0
oh wait it should be 2x^2 = 16 -10x. I'll try to solve it later
16 less than 10 times the number is translated as 10x-16. You will have it as 2x^2 = 10x - 16.. dividing the whole equation by 2 you'll have x^2-5x+8=0.. it can't be factored using square property hence you only have 1,2,4 and 8 as the factors of 8 and none would satisfy the middle term. using quadratic formula to find the factors, you will have the factors as [x-(5/2+sqrt7/2i)] and [x-(5/2-sqrt7/2i)]... (-_-)!
haha sorry about it... then my first equation is right than my second. I can't re edit my answer below

## Answers

2014-11-06T13:18:22+08:00
Let me try to solve it.

So twice the square of a number:

2x²

and

16 less than 10 times the number

16 - 10x

Let's combine both

2x² = 16 - 10x

Move right expression to the left and change sign

2x² +10x -16 = 0

We may now use quadratic formula for this.

x = (-b±√b²-4ac)/2a

where a = 2, b = 10 and c = -16

Replace a, b and c

x = (-10±√10² - 4(2 * -16))/2(2)

Multiply 2 and -16, 2 and 2, and get the square of 10

x = (-10±√100 - 4(-32))/4

Multiply -4 and -32

x = (-10±√100 + 128)/4

Add 100 and 128

x = (-10±√228)/4

Get square root of 228

x = (-10±15.0996688705415)/4

Break up expression

x = (-10 + 15.0996688705415)/4

Add

x = 5.0996688705415/4

Divide

x = 1.274917217635375

---

x = (-10 - 15.0996688705415)/4

Subtract

x = -25.0996688705415/4

Divide

x = -6.274917217635375

Now to check:

We are going to use the positive result except of the negative.

2(1.274917217635375)² = 16 - 10(1.274917217635375)

2(1.625413911823126143) = 16 - 12.74917217635375

3.250827823646252286 = 3.25082782364625

Almost the same as you can see except of the 2286 in the last from the left side.

I hope it helps.