Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
t1=8−46,t2=8+46
Alternative Form
t1≈−1.797959,t2≈17.797959
Evaluate
t2−16t−32=0
Substitute a=1,b=−16 and c=−32 into the quadratic formula t=2a−b±b2−4ac
t=216±(−16)2−4(−32)
Simplify the expression
More Steps

Evaluate
(−16)2−4(−32)
Multiply the numbers
More Steps

Evaluate
4(−32)
Multiplying or dividing an odd number of negative terms equals a negative
−4×32
Multiply the numbers
−128
(−16)2−(−128)
Rewrite the expression
162−(−128)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
162+128
Evaluate the power
256+128
Add the numbers
384
t=216±384
Simplify the radical expression
More Steps

Evaluate
384
Write the expression as a product where the root of one of the factors can be evaluated
64×6
Write the number in exponential form with the base of 8
82×6
The root of a product is equal to the product of the roots of each factor
82×6
Reduce the index of the radical and exponent with 2
86
t=216±86
Separate the equation into 2 possible cases
t=216+86t=216−86
Simplify the expression
More Steps

Evaluate
t=216+86
Divide the terms
More Steps

Evaluate
216+86
Rewrite the expression
22(8+46)
Reduce the fraction
8+46
t=8+46
t=8+46t=216−86
Simplify the expression
More Steps

Evaluate
t=216−86
Divide the terms
More Steps

Evaluate
216−86
Rewrite the expression
22(8−46)
Reduce the fraction
8−46
t=8−46
t=8+46t=8−46
Solution
t1=8−46,t2=8+46
Alternative Form
t1≈−1.797959,t2≈17.797959
Show Solution
