How do you solve this equation: 3x-5*√x=2. (√= Is a square root sign)
is that the original equation? or is it somewhere along the way of one?
3x-5*√x-2=0
3x-3*√x-2*√x-2=0
To solve the equation 3x - 5√x = 2, we can follow these steps:
Step 1: Move the square root term to one side of the equation.
Add 5√x to both sides:
3x = 2 + 5√x
Step 2: Isolate the square root term.
Subtract 2 from both sides:
3x - 2 = 5√x
Step 3: Square both sides of the equation to eliminate the square root.
(3x - 2)^2 = (5√x)^2
(3x - 2)(3x - 2) = 25x
Step 4: Expand and simplify.
9x^2 - 6x - 6x + 4 = 25x
9x^2 - 12x + 4 = 25x
Step 5: Move all terms to one side to form a quadratic equation.
Subtract 25x from both sides:
9x^2 - 12x + 4 - 25x = 0
9x^2 - 37x + 4 = 0
Step 6: Solve the quadratic equation.
Using factoring, the equation can be factored into:
(3x - 1)(3x - 4) = 0
Setting each factor equal to zero:
3x - 1 = 0
3x = 1
x = 1/3
3x - 4 = 0
3x = 4
x = 4/3
Step 7: Check the solutions.
Substitute x = 1/3 back into the original equation:
3(1/3) - 5√(1/3) = 2
1 - 5√(1/3) = 2
-5√(1/3) = 1
√(1/3) = -1/5
Since the square root cannot be negative, x = 1/3 is not a valid solution.
Substitute x = 4/3 back into the original equation:
3(4/3) - 5√(4/3) = 2
4 - 5√(4/3) = 2
-5√(4/3) = -2
√(4/3) = 2/5
Thus, the solution to the equation 3x - 5√x = 2 is x = 4/3.
To solve the equation 3x - 5√x = 2, we can follow these steps:
Step 1: Move the term with the square root to one side of the equation by adding 5√x to both sides:
3x = 2 + 5√x
Step 2: Isolate the term with the square root by moving the other terms to the other side of the equation:
3x - 5√x = 2
Step 3: Square both sides of the equation to eliminate the square root:
(3x - 5√x)^2 = 2^2
(3x - 5√x)(3x - 5√x) = 4
9x^2 - 15x√x - 15x√x + 25x = 4
9x^2 - 30x√x + 25x - 4 = 0
Step 4: Simplify the equation if needed:
9x^2 - 30x√x + 25x - 4 = 0
Now we have a quadratic equation in terms of x and √x. We can solve this quadratic equation for x using either factoring, completing the square, or the quadratic formula. However, since the presence of √x makes factoring difficult, we can use a variable substitution to make it easier.
Let's assume that √x = t. Now we can rewrite the equation in terms of t:
9t^2 - 30t√t + 25√t - 4 = 0
Step 5: Solve the quadratic equation in terms of t. We can then substitute back to find x.
At this point, we have transformed the original equation into a quadratic equation involving t. To find the values of t, we can proceed using various methods. For example, we may use factoring or the quadratic formula to solve the quadratic equation:
9t^2 - 30t√t + 25√t - 4 = 0
Once we find the solutions for t, we can substitute them back into the equation √x = t to find the values of x.
Please note that without further information or constraints, there may be multiple solutions for x or t.