solve the square root of 2a-1 is equal to 5
solve c- the square root of c is equal to 30
a.
2a-1 = 5
Add one to each side:
2a -1+1 = 5+1
2a = 6
a = 6/2 = 3
b.
√c = 30
square both sides
c = 30^2 = 900
for the first question it's the square root of 2a -1 not just 2a -1
and for the second question its c- the square root of c = 30 not just the square root of c = 30
Sorry, here it is, square both side before working on it:
√(2a-1) = 5
square both sides:
2a-1 = 25
Add one to each side:
2a -1+1 = 25+1
2a = 26
a = 26/2 = 13
To solve the equations, we need to isolate the variable on one side of the equation. Let's solve each equation step by step.
1. Square root of 2a - 1 = 5:
To isolate the square root term, begin by adding 1 to both sides of the equation:
Square root of 2a - 1 + 1 = 5 + 1
This simplifies to:
Square root of 2a = 6
Next, square both sides of the equation to eliminate the square root:
(Square root of 2a)^2 = 6^2
This reduces to:
2a = 36
Finally, divide both sides of the equation by 2 to solve for 'a':
2a/2 = 36/2
The solution is:
a = 18
2. c - square root of c = 30:
Here, we will proceed similarly to isolate the square root term.
Add the square root of c to both sides of the equation:
c - square root of c + square root of c = 30 + square root of c
This simplifies to:
c = 30 + square root of c
Next, square both sides of the equation to eliminate the square root:
c^2 = (30 + square root of c)^2
Expanding the right side gives:
c^2 = 900 + 60 * square root of c + c
Rearrange the equation:
c^2 - c - 900 = 60 * square root of c
To isolate the square root, subtract c and 900 from both sides:
c^2 - c - 900 - c - 900 = 60 * square root of c - c - 900
This simplifies to:
c^2 - 2c - 1800 = 60 * square root of c - c
Now, we will square both sides once more:
(c^2 - 2c - 1800)^2 = (60 * square root of c - c)^2
This results in a quadratic equation. Expanding both sides gives:
c^4 - 4c^3 - 3560c^2 + 7200c + 3240000 = 3600c - 120c * square root of c + c^2
Rearrange this equation:
c^4 - 4c^3 - 3561c^2 - 3579c - 3240000 = -120c * square root of c
To solve this equation, you can either use numerical methods or approximation techniques. The solution may not be an integer or rational number.
Alternatively, you could use a graphing calculator or software to solve for the value of c.
Please note that due to the complexity of this equation, the solution process may involve approximate methods to find a numerical value for c.