Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=63−39,x2=63+39
Alternative Form
x1≈−0.540833,x2≈1.540833
Evaluate
6x2−6x−5=0
Substitute a=6,b=−6 and c=−5 into the quadratic formula x=2a−b±b2−4ac
x=2×66±(−6)2−4×6(−5)
Simplify the expression
x=126±(−6)2−4×6(−5)
Simplify the expression
More Steps

Evaluate
(−6)2−4×6(−5)
Multiply
More Steps

Multiply the terms
4×6(−5)
Rewrite the expression
−4×6×5
Multiply the terms
−120
(−6)2−(−120)
Rewrite the expression
62−(−120)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
62+120
Evaluate the power
36+120
Add the numbers
156
x=126±156
Simplify the radical expression
More Steps

Evaluate
156
Write the expression as a product where the root of one of the factors can be evaluated
4×39
Write the number in exponential form with the base of 2
22×39
The root of a product is equal to the product of the roots of each factor
22×39
Reduce the index of the radical and exponent with 2
239
x=126±239
Separate the equation into 2 possible cases
x=126+239x=126−239
Simplify the expression
More Steps

Evaluate
x=126+239
Divide the terms
More Steps

Evaluate
126+239
Rewrite the expression
122(3+39)
Cancel out the common factor 2
63+39
x=63+39
x=63+39x=126−239
Simplify the expression
More Steps

Evaluate
x=126−239
Divide the terms
More Steps

Evaluate
126−239
Rewrite the expression
122(3−39)
Cancel out the common factor 2
63−39
x=63−39
x=63+39x=63−39
Solution
x1=63−39,x2=63+39
Alternative Form
x1≈−0.540833,x2≈1.540833
Show Solution
