Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=105−35,x2=105+35
Alternative Form
x1≈−0.17082,x2≈1.17082
Evaluate
100x2−100x−11=9
Move the expression to the left side
100x2−100x−20=0
Substitute a=100,b=−100 and c=−20 into the quadratic formula x=2a−b±b2−4ac
x=2×100100±(−100)2−4×100(−20)
Simplify the expression
x=200100±(−100)2−4×100(−20)
Simplify the expression
More Steps

Evaluate
(−100)2−4×100(−20)
Multiply
More Steps

Multiply the terms
4×100(−20)
Rewrite the expression
−4×100×20
Multiply the terms
−8000
(−100)2−(−8000)
Rewrite the expression
1002−(−8000)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1002+8000
Evaluate the power
10000+8000
Add the numbers
18000
x=200100±18000
Simplify the radical expression
More Steps

Evaluate
18000
Write the expression as a product where the root of one of the factors can be evaluated
3600×5
Write the number in exponential form with the base of 60
602×5
The root of a product is equal to the product of the roots of each factor
602×5
Reduce the index of the radical and exponent with 2
605
x=200100±605
Separate the equation into 2 possible cases
x=200100+605x=200100−605
Simplify the expression
More Steps

Evaluate
x=200100+605
Divide the terms
More Steps

Evaluate
200100+605
Rewrite the expression
20020(5+35)
Cancel out the common factor 20
105+35
x=105+35
x=105+35x=200100−605
Simplify the expression
More Steps

Evaluate
x=200100−605
Divide the terms
More Steps

Evaluate
200100−605
Rewrite the expression
20020(5−35)
Cancel out the common factor 20
105−35
x=105−35
x=105+35x=105−35
Solution
x1=105−35,x2=105+35
Alternative Form
x1≈−0.17082,x2≈1.17082
Show Solution
