Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=36−51,x2=36+51
Alternative Form
x1≈−0.380476,x2≈4.380476
Evaluate
3x2−12x−5=0
Substitute a=3,b=−12 and c=−5 into the quadratic formula x=2a−b±b2−4ac
x=2×312±(−12)2−4×3(−5)
Simplify the expression
x=612±(−12)2−4×3(−5)
Simplify the expression
More Steps

Evaluate
(−12)2−4×3(−5)
Multiply
More Steps

Multiply the terms
4×3(−5)
Rewrite the expression
−4×3×5
Multiply the terms
−60
(−12)2−(−60)
Rewrite the expression
122−(−60)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
122+60
Evaluate the power
144+60
Add the numbers
204
x=612±204
Simplify the radical expression
More Steps

Evaluate
204
Write the expression as a product where the root of one of the factors can be evaluated
4×51
Write the number in exponential form with the base of 2
22×51
The root of a product is equal to the product of the roots of each factor
22×51
Reduce the index of the radical and exponent with 2
251
x=612±251
Separate the equation into 2 possible cases
x=612+251x=612−251
Simplify the expression
More Steps

Evaluate
x=612+251
Divide the terms
More Steps

Evaluate
612+251
Rewrite the expression
62(6+51)
Cancel out the common factor 2
36+51
x=36+51
x=36+51x=612−251
Simplify the expression
More Steps

Evaluate
x=612−251
Divide the terms
More Steps

Evaluate
612−251
Rewrite the expression
62(6−51)
Cancel out the common factor 2
36−51
x=36−51
x=36+51x=36−51
Solution
x1=36−51,x2=36+51
Alternative Form
x1≈−0.380476,x2≈4.380476
Show Solution
