To solve: x22+x20=110

Question

einfachmoipf · Accepted Answer

Calculation:
Multiply by 20 on both sides,

20 (\frac{x^{2}}{2} + \frac{x}{20}) = \frac{1}{10} \cdot 20

By distributive property,

20 (\frac{x^{2}}{2} + \frac{x}{20}) = 20 \cdot \frac{x^{2}}{2} + 20 \cdot \frac{x}{20}

20 (\frac{x^{2}}{2} + \frac{x}{20}) = 10 x^{2} + x

\frac{1}{10} \cdot 20 = 2

10 x^{2} + x = 2

Subtract 2 on both sides,

10 x^{2} + x - 2 = 2 - 2

10 x^{2} + x - 2 = 0

Split the middle term

+ x as + 5 x and - 4 x

.
Replace

+ x with - 4 x + 5 x \in 10 x^{2} + x - 2 = 0

10 x^{2} - 4 x + 5 x - 2 = 0

The above equation can be written as

2 x \cdot 5 x - 2 \cdot 2 x + 1 \cdot 5 x - 1 \cdot 2

Apply distributive property for first two terms and last two terms,

2 x \cdot 5 x - 2 \cdot 2 x + 1 \cdot 5 x - 1 \cdot 2 = 2 x (5 x - 2) + 1 (5 x - 2)

Again apply distributive property for

2 x (5 x - 2) + 1 (5 x - 2)

2 x (5 x - 2) + 1 (5 x - 2) = (2 x + 1) (5 x - 2)

So the factors are

(2 x + 1) and (5 x - 2)

10 x^{2} + x - 2 = (2 x + 1) (5 x - 2)

To find the value of x,
Take

5 x - 2 = 0

Add 2 on both sides,

5 x - 2 + 2 = 0 + 2

Add the like terms,

5 x = 2

Divide by 5 on both sides,

\frac{5 x}{5} = \frac{2}{5}

x = \frac{2}{5}

Take

2 x + 1 = 0

Subtract 1 on both sides,

2 x + 1 - 1 = 0 - 1

Add the like terms,

2 x = - 1

Divide by 2 on both sides,

Paul Mitchell · Accepted Answer

Step 1: Simplify both sides of the equation.  12x2+120x=110  Step 2: Subtract 1/10 from both sides.  12x2+120x−110=110−110  12x2+120x+−110=0  For this equation: a=0.5,b=0.05,c=−0.1   0.5x2+0.05x±0.1=0   Step 3: Use quadratic formula with a=0.5,b=0.05,c=−0.1.  x=−b±b2−4ac2a  x=−(0.05)±(0.05)2−4(0.5)(−0.1)2(0.5)  x=−0.05±0.20251  x=0.4,−0.5  Answer: x=0.4,−0.5

karton · Accepted Answer

12x2+120x=11012x2+120x−110=110−11012x2+120x−110=0x=−120±(120)2−4×(12)(−110)2×(12)x=−120±1400−4×(12)(−12)2×(12)x=−120±1400−2(−110)2×(12)x=−120±1400+152×(12)x=−120±814002×(12)x=−120±9202×(12)x=−120±9201x=251x=25x=−121x=−12x=25x=−12

To solve: \frac{x^{2}}{2}+\frac{x}{20}=\frac{1}{10}

Answered question

Answer & Explanation

New Questions in Algebra I