Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
ff2−650−750f
Evaluate
f−f650−750
Reduce fractions to a common denominator
ff×f−f650−f750f
Write all numerators above the common denominator
ff×f−650−750f
Solution
ff2−650−750f
Show Solution
Find the excluded values
f=0
Evaluate
f−f650−750
Solution
f=0
Show Solution
Find the roots
f1=375−55651,f2=375+55651
Alternative Form
f1≈−0.865667,f2≈750.865667
Evaluate
f−f650−750
To find the roots of the expression,set the expression equal to 0
f−f650−750=0
Find the domain
f−f650−750=0,f=0
Calculate
f−f650−750=0
Subtract the terms
More Steps
Simplify
f−f650
Reduce fractions to a common denominator
ff×f−f650
Write all numerators above the common denominator
ff×f−650
Multiply the terms
ff2−650
ff2−650−750=0
Subtract the terms
More Steps
Simplify
ff2−650−750
Reduce fractions to a common denominator
ff2−650−f750f
Write all numerators above the common denominator
ff2−650−750f
ff2−650−750f=0
Cross multiply
f2−650−750f=f×0
Simplify the equation
f2−650−750f=0
Rewrite in standard form
f2−750f−650=0
Substitute a=1,b=−750 and c=−650 into the quadratic formula f=2a−b±b2−4ac
f=2750±(−750)2−4(−650)
Simplify the expression
More Steps
Evaluate
(−750)2−4(−650)
Multiply the numbers
More Steps
Evaluate
4(−650)
Multiplying or dividing an odd number of negative terms equals a negative
−4×650
Multiply the numbers
−2600
(−750)2−(−2600)
Rewrite the expression
7502−(−2600)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
7502+2600
f=2750±7502+2600
Simplify the radical expression
More Steps
Evaluate
7502+2600
Add the numbers
565100
Write the expression as a product where the root of one of the factors can be evaluated
100×5651
Write the number in exponential form with the base of 10
102×5651
The root of a product is equal to the product of the roots of each factor
102×5651
Reduce the index of the radical and exponent with 2
105651
f=2750±105651
Separate the equation into 2 possible cases
f=2750+105651f=2750−105651
Simplify the expression
More Steps
Evaluate
f=2750+105651
Divide the terms
More Steps
Evaluate
2750+105651
Rewrite the expression
22(375+55651)
Reduce the fraction
375+55651
f=375+55651
f=375+55651f=2750−105651
Simplify the expression
More Steps
Evaluate
f=2750−105651
Divide the terms
More Steps
Evaluate
2750−105651
Rewrite the expression
22(375−55651)
Reduce the fraction
375−55651
f=375−55651
f=375+55651f=375−55651
Check if the solution is in the defined range
f=375+55651f=375−55651,f=0
Find the intersection of the solution and the defined range
f=375+55651f=375−55651
Solution
f1=375−55651,f2=375+55651
Alternative Form
f1≈−0.865667,f2≈750.865667
Show Solution