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# Solve the inequality $1414\cdot 20x+x^2\leq 60400$

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##  Final answer to the problem

$x\leq \sqrt{200000000}-14140$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Prove from LHS (left-hand side)
Can't find a method? Tell us so we can add it.
1

Multiply $1414$ times $20$

$28280x+x^2\leq 60400$

Learn how to solve problems step by step online.

$28280x+x^2\leq 60400$

Learn how to solve problems step by step online. Solve the inequality 1414*20x+x^2<=60400. Multiply 1414 times 20. Factor the polynomial 28280x+x^2. Add and subtract \left(\frac{b}{2}\right)^2, replacing b by it's value 28280. Now, we can factor x^2+28280x+199939600 as a squared binomial of the form \left(x+\frac{b}{2}\right)^2. Moving the term -199939600 to the other side of the inequation with opposite sign.

##  Final answer to the problem

$x\leq \sqrt{200000000}-14140$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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a
b
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w
x
y
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(◻)
+
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◻/◻
/
÷
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch