Solve: x= sqrt(10x-4-2)
The last time I checked, -4 -2 = 6.
Check to make sure you did not omit some parentheses that would change the maning of what you wrote
Square both sides of the equation and solve the resulting quadratic.
x^2 - 10x +6 = 0
The problem is solve x= sqrt10x-4-2
To solve for x, we can follow these steps:
Step 1: Isolate the square root term.
Start by subtracting x from both sides of the equation:
x - x = sqrt(10x - 4 - 2) - x
This simplifies to:
0 = sqrt(10x - 4 - 2) - x
Step 2: Square both sides of the equation.
Squaring both sides will eliminate the square root:
0^2 = (sqrt(10x - 4 - 2) - x)^2
Simplifying the equation further:
0 = (10x - 6 - 2sqrt(10x - 4 - 2) + x^2 - 2x(sqrt(10x - 4 - 2)))
Step 3: Combine like terms.
Rearrange the equation in descending order of powers of x:
x^2 + (10 - 2(sqrt(10x - 4 - 2)))x - 6 - 2sqrt(10x - 4 - 2) = 0
Step 4: Solve the quadratic equation.
Now we have a quadratic equation in standard form (ax^2 + bx + c = 0), where:
a = 1
b = 10 - 2(sqrt(10x - 4 - 2))
c = -6 - 2sqrt(10x - 4 - 2)
At this point, we can solve the quadratic equation using factoring, completing the square, or the quadratic formula. However, since the equation is quite complicated, it is difficult to solve it algebraically. In such cases, numerical methods like approximation or iteration can be used to find an estimate or a solution.
Please note that the equation you provided may have been mistyped, as solving it algebraically leads to complex expressions.