Move 100100 to the left side of the equation by subtracting it from both sides.
5x+x2−100>05x+x2-100>0
Convert the inequality to an equation.
5x+x2−100=05x+x2-100=0
utilize the quadratic formula to find the solutions.
−b±√b2−4(ac)2a-b±b2-4(ac)2a
Substitute the values a=1a=1, b=5b=5, and c=−100c=-100 into the quadratic formula and solve for xx.
−5±√52−4⋅(1⋅−100)2⋅1-5±52-4⋅(1⋅-100)2⋅1
x=−5±5√172x=-5±5172
Consolidate the solutions.
x=−5−5√172,−5+5√172x=-5-5172,-5+5172
Use each root to create test intervals.
x<−5+5√172x<-5+5172
−5+5√172<x<−5−5√172-5+5172<x<-5-5172
x>−5−5√172x>-5-5172
Choose a test worth from each interval and plug this value into the original inequality to determine which interval satisfy the inequality.
x<−5+5√172x<-5+5172 True
−5+5√172<x<−5−5√172-5+5172<x<-5-5172 False
x>−5−5√172x>-5-5172 True
The solution consists of all of the proper intervals.
x<−5+5√172x<-5+5172 or x>−5−5√172x>-5-5172
The result can show in multiple forms.
Inequality Form:
x<−5+5√172orx>−5−5√172x<-5+5172orx>-5-5172
Interval Notation:
(−∞,−5+5√172)∪(−5−5√172,∞)
if 5x + x² > 100, in that case x is not Equation
An equation is a mathematical declaration with an equal sign between two expressions with similar values. For example, if 5x + x² > 100, then x is not there are different types of equations like linear, quadratic, cubic etc. Let’s learn more about mathematical equations in this article.
Equations are mathematical statements that contain two algebraic expressions on either side of an equal sign (=). Shows the equality relationship between the expression written on the left and the expression written on the right. In any math equation we have L.H.S = R.H.S (left side = right side). 5x+x2−100>05x+x2-100>0
Equations can find the value of an unknown variable that represents an unknown quantity. If the declaration doesn’t contain an equals sign, it means it’s not an equation. Instead, it is considered an expression. You will discover the difference between equations and look in this article’s later section.
Check out the examples below. These give you an idea of the meaning of an equation in mathematics.
5x+x2−100=05x+x2-100=0
−5±√52−4⋅(1⋅−100)2⋅1-5±52-4⋅(1⋅-100)2⋅1
Now let’s move on and study the parts of a mathematical equation.
An equation has different parts, including coefficients, variables, operators, constants, terms, expressions, and an equals sign. There must be an “=” sign and terms on both sides when we write an equation. In addition, both sides must be equal to each other.
An equation is like a scale with equal weights on both sides. It still applies if we add or subtract the same number on both sides of an equation. Likewise, even if we multiply or divide the same number into both sides of an equation, it still applies.
Step 1: Put all terms with variables on one side and all constants on the other side of the equation by doing arithmetic operations on both sides.
2 Step: Combine all equal terms (terms containing the same variable with the same exponent) by adding or subtracting.
Step 3: Simplify and get the answer(If 5x + x² >100, then x is not)
Let’s take another example of a basic equation: 3x – 20 = 7. To shift all the constants to the right, we need to add 20 to both sides. This imply 3x – 20 + 20 = 7 + 20, which simplifies to 3x = 27. Now divide both sides by 3. This gives x = 9, which is the required solution to the equation.
Depending on the degree, the equations can classify into three types. The following are the three types of equations in mathematics:
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2a-b±b2-4(ac)2a Substitute the values a=1a=1, b=5b=5, and c=−100c=-100 into the quadratic formula and solve for xx. −5±√52−4⋅(1⋅−100)2⋅1-5±52-4⋅(1⋅-100)2⋅1 Solution 1 : For if 5x + x² > 100, then […]){kind=link}
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