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2 years ago

If 2x• 3x +(2•3 )x +6x= 648, find x.

Mathematics

2 answers:

ycow [4]2 years ago

7 0

(2*3)x= 6x
2x*3x=6x
6x+6x+6x=648
648/36

klasskru [66]2 years ago

4 0

Answer:

x = -1 ± √109

Step-by-step explanation:

2x • 3x + (2 • 3)x + 6x = 648

According to PEMDAS (parentheses/exponents | multiplication/division | addition/subtraction), we should solve the parentheses first.

(2 • 3) = 6

Now we have:

2x • 3x + (6)x + 6x = 648

Now let's multiply.

2x • 3x = 6x²

6 • x = 6x

Now we have.

6x² + 6x + 6x = 648

Combine like terms.

6x² + 12x = 648

Let's factor out a 6.

6(x² + 2x) = 648

Divide both sides by 6.

x² + 2x = 108

Let's use completing the square.

Our equation is in a² + bx = c form.

Divide b by 2.

2/2 = 1

Then square it.

1² = 1

Add 1 to both sides.

x² + 2x + 1 = 108 + 1

Simplify.

x² + 2x + 1 = 109

Now we want to factor the left side. A shortcut is just to use b/2.

(x + 1)² = 109

Take the square root of both sides.

x + 1 = ±√109

The square root is as simplified as possible.

Subtract 1 from both sides.

x = -1 ± √109

Hope this helps!

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Answer:

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$\int\limits^{}_{} {x} \, dx = \frac{x^2}{2}$

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Then our integral is:

$\int\limits^2_{-1} {(x^2 + 1 - x)} \, dx = (\frac{2^3}{2} + 2 - \frac{2^2}{2}) - (\frac{(-1)^3}{3} + (-1) - \frac{(-1)^2}{2} )$

The right side is equal to:

$(4 + 2 - 2) - ( -1/3 - 1 - 1/2) = 4 + 1/3 + 1 + 1/2 = 5 + 2/6 + 3/6 = 5 + 5/6$

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