Answer:
x = -1
Explanation:
The terms under the square root must be positive or zero
4t + 5 ≥ 0
4t ≥ -5
4/4 t ≥ -5/4
t ≥ -5/4
t +5 ≥ 0
t ≥ -5
if we match the two conditions we have that t ≥ -5/4
Now we can elevate at the power of 2 for eliminate the roots
4t + 5 = 9 + t + 5 -3 · 2 ·√(t+5)
4t + 5 = 9 + t + 5 - 6√(t+5)
4t - t -9 = -6√(t+5)
3t-9 = -6√(t+5)
Multiply per -1
-3t + 9 = 6√(t+5)
Divide by 3 for simplify
-t + 3 = 2√(t+5)
Elevate by power of 2 for eliminate the root
t² + 9 + 2 · (-t · 3) = 4(t+5)
t² + 9 - 6t = 4t + 20
t² - 6t - 4t + 9 - 20 = 0
t² - 10t - 11 = 0
Now we have to find two number whose sum is -10 and whose product is -11
The two numbers are -11 and 1
We can rewrite the expression in this way
(t-11)(t+1) = 0
A product is equal to 0 when one of the factors is 0, so we can solve separately in this way:
t - 11 = 0
t = 11
t + 1 = 0
t = -1
At the end we have to check the solutions by substitute t with the number that we have found
√(4 · 11 + 5) = 3 - √(11+5)
√(44+5) = 3 - √(16)
√(49) = 3 - 4
7 = -1 (false)
√(4 · -1 + 5) = 3 - √(-1 +5)
√ ( -4 + 5) = 3 - √(4)
√ 1 = 3 - 2
1 = 1 (true)