Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=21−21,x2=21+21
Alternative Form
x1≈−1.791288,x2≈2.791288
Evaluate
x×51(x−1)=1
Use the commutative property to reorder the terms
51x(x−1)=1
Expand the expression
More Steps

Evaluate
51x(x−1)
Apply the distributive property
51x×x−51x×1
Multiply the terms
51x2−51x×1
Any expression multiplied by 1 remains the same
51x2−51x
51x2−51x=1
Move the expression to the left side
51x2−51x−1=0
Multiply both sides
5(51x2−51x−1)=5×0
Calculate
x2−x−5=0
Substitute a=1,b=−1 and c=−5 into the quadratic formula x=2a−b±b2−4ac
x=21±(−1)2−4(−5)
Simplify the expression
More Steps

Evaluate
(−1)2−4(−5)
Evaluate the power
1−4(−5)
Multiply the numbers
More Steps

Evaluate
4(−5)
Multiplying or dividing an odd number of negative terms equals a negative
−4×5
Multiply the numbers
−20
1−(−20)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+20
Add the numbers
21
x=21±21
Separate the equation into 2 possible cases
x=21+21x=21−21
Solution
x1=21−21,x2=21+21
Alternative Form
x1≈−1.791288,x2≈2.791288
Show Solution
