Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=45−209,x2=45+209
Alternative Form
x1≈−2.364208,x2≈4.864208
Evaluate
x(2x−5)=23
Expand the expression
More Steps

Evaluate
x(2x−5)
Apply the distributive property
x×2x−x×5
Multiply the terms
More Steps

Evaluate
x×2x
Use the commutative property to reorder the terms
2x×x
Multiply the terms
2x2
2x2−x×5
Use the commutative property to reorder the terms
2x2−5x
2x2−5x=23
Move the expression to the left side
2x2−5x−23=0
Substitute a=2,b=−5 and c=−23 into the quadratic formula x=2a−b±b2−4ac
x=2×25±(−5)2−4×2(−23)
Simplify the expression
x=45±(−5)2−4×2(−23)
Simplify the expression
More Steps

Evaluate
(−5)2−4×2(−23)
Multiply
More Steps

Multiply the terms
4×2(−23)
Rewrite the expression
−4×2×23
Multiply the terms
−184
(−5)2−(−184)
Rewrite the expression
52−(−184)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
52+184
Evaluate the power
25+184
Add the numbers
209
x=45±209
Separate the equation into 2 possible cases
x=45+209x=45−209
Solution
x1=45−209,x2=45+209
Alternative Form
x1≈−2.364208,x2≈4.864208
Show Solution
