Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x+y=15
-
Equation -(-y+4)+2*y+1=0
-
Equation 11-5(2x+1)=41-9x
- Equation 2*x^2+50=0
- Express {x} in terms of y where:
- -16*x-20*y=-13
- 4*x+5*y=7
- -5*x+7*y=-18
- -11*x-20*y=9
-
Identical expressions
- sqrt(5x- sixteen)= three
- square root of (5x minus 16) equally 3
- square root of (5x minus sixteen) equally three
- √(5x-16)=3
- sqrt5x-16=3
-
Similar expressions
- sqrt(5x+16)=3
sqrt(5x-16)=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{5 x - 16} = 3$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{5 x - 16}\right)^{2} = 3^{2}$$
or
$$5 x - 16 = 9$$
Move free summands (without x)
from left part to right part, we given:
$$5 x = 25$$
Divide both parts of the equation by 5
We get the answer: x = 5
The final answer:
$$x_{1} = 5$$
$$\sqrt{5 x - 16} = 3$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{5 x - 16}\right)^{2} = 3^{2}$$
or
$$5 x - 16 = 9$$
Move free summands (without x)
from left part to right part, we given:
$$5 x = 25$$
Divide both parts of the equation by 5
x = 25 / (5)
We get the answer: x = 5
The final answer:
$$x_{1} = 5$$
Numerical answer
[src]
x1 = 5.0
x2 = 5.00000000000004 + 8.43766451423806e-14*i
x3 = 5.0 + 7.89181195440627e-16*i
x4 = 5.0 + 3.87764419367184e-18*i
x4 = 5.0 + 3.87764419367184e-18*i