Nickahcabiaoidn
Answered

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

Sagot :

Alvedeguzidn
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.
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