Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for a
Solve for t
a=0a=−t−1ta=t+1t
Evaluate
a4t4=(at)2(a−t)2
Multiply the terms
a4t4=(at(a−t))2
Rewrite the expression
t4a4=(ta(a−t))2
Move the expression to the left side
t4a4−(ta(a−t))2=0
Add or subtract both sides
More Steps
Calculate
−(ta(a−t))2
Evaluate
ta(a−t)
Apply the distributive property
ta×a−tat
Multiply the terms
ta2−tat
Multiply the terms
More Steps
Evaluate
t×t
Multiply the terms with the same base by adding their exponents
t1+1
Add the numbers
t2
ta2−t2a
t4a4−t2a4+2t3a3−t4a2=0
Collect like terms by calculating the sum or difference of their coefficients
(t4−t2)a4+2t3a3−t4a2=0
Factor the expression
t2a2((t2−1)a2+2ta−t2)=0
Divide both sides
a2((t2−1)a2+2ta−t2)=0
Separate the equation into 2 possible cases
a2=0(t2−1)a2+2ta−t2=0
The only way a power can be 0 is when the base equals 0
a=0(t2−1)a2+2ta−t2=0
Solution
More Steps
Evaluate
(t2−1)a2+2ta−t2=0
Expand the expression
t2a2−a2+2ta−t2=0
Factor the expression
More Steps
Evaluate
t2a2−a2+2ta−t2
Calculate
t2a2−t2a+ta2+t2a−t2+ta−ta2+ta−a2
Rewrite the expression
tata−tat+ta×a+t×ta−t×t+ta−ata+at−a×a
Factor out ta from the expression
ta(ta−t+a)+t×ta−t×t+ta−ata+at−a×a
Factor out t from the expression
ta(ta−t+a)+t(ta−t+a)−ata+at−a×a
Factor out −a from the expression
ta(ta−t+a)+t(ta−t+a)−a(ta−t+a)
Factor out ta−t+a from the expression
(ta+t−a)(ta−t+a)
(ta+t−a)(ta−t+a)=0
When the product of factors equals 0,at least one factor is 0
ta+t−a=0ta−t+a=0
Solve the equation for a
More Steps
Evaluate
ta+t−a=0
Collect like terms by calculating the sum or difference of their coefficients
(t−1)a+t=0
Move the constant to the right side
(t−1)a=0−t
Removing 0 doesn't change the value,so remove it from the expression
(t−1)a=−t
Divide both sides
t−1(t−1)a=t−1−t
Divide the numbers
a=t−1−t
Use b−a=−ba=−ba to rewrite the fraction
a=−t−1t
a=−t−1tta−t+a=0
Solve the equation for a
More Steps
Evaluate
ta−t+a=0
Collect like terms by calculating the sum or difference of their coefficients
(t+1)a−t=0
Move the constant to the right side
(t+1)a=0+t
Removing 0 doesn't change the value,so remove it from the expression
(t+1)a=t
Divide both sides
t+1(t+1)a=t+1t
Divide the numbers
a=t+1t
a=−t−1ta=t+1t
a=0a=−t−1ta=t+1t
Show Solution
