Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
t1=−941+1505,t2=94−1+1505
Alternative Form
t1≈−0.423344,t2≈0.402067
Evaluate
16−2t=t×94t
Multiply
More Steps

Evaluate
t×94t
Multiply the terms
t2×94
Use the commutative property to reorder the terms
94t2
16−2t=94t2
Swap the sides
94t2=16−2t
Move the expression to the left side
94t2−16+2t=0
Rewrite in standard form
94t2+2t−16=0
Substitute a=94,b=2 and c=−16 into the quadratic formula t=2a−b±b2−4ac
t=2×94−2±22−4×94(−16)
Simplify the expression
t=188−2±22−4×94(−16)
Simplify the expression
More Steps

Evaluate
22−4×94(−16)
Multiply
More Steps

Multiply the terms
4×94(−16)
Rewrite the expression
−4×94×16
Multiply the terms
−6016
22−(−6016)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+6016
Evaluate the power
4+6016
Add the numbers
6020
t=188−2±6020
Simplify the radical expression
More Steps

Evaluate
6020
Write the expression as a product where the root of one of the factors can be evaluated
4×1505
Write the number in exponential form with the base of 2
22×1505
The root of a product is equal to the product of the roots of each factor
22×1505
Reduce the index of the radical and exponent with 2
21505
t=188−2±21505
Separate the equation into 2 possible cases
t=188−2+21505t=188−2−21505
Simplify the expression
More Steps

Evaluate
t=188−2+21505
Divide the terms
More Steps

Evaluate
188−2+21505
Rewrite the expression
1882(−1+1505)
Cancel out the common factor 2
94−1+1505
t=94−1+1505
t=94−1+1505t=188−2−21505
Simplify the expression
More Steps

Evaluate
t=188−2−21505
Divide the terms
More Steps

Evaluate
188−2−21505
Rewrite the expression
1882(−1−1505)
Cancel out the common factor 2
94−1−1505
Use b−a=−ba=−ba to rewrite the fraction
−941+1505
t=−941+1505
t=94−1+1505t=−941+1505
Solution
t1=−941+1505,t2=94−1+1505
Alternative Form
t1≈−0.423344,t2≈0.402067
Show Solution
