can someone show me how to solve an equation algerbracially
x=sqrtx+10+2
Are you just taking the square root of the x?
If so:
x - square root of x = 12
or is it x = sqrt(x+10) + 2?
if so: x -sqrt(x+10) = 2
Square both sides:
Then solve.
sorry its x=sqrt(x+10)+2
i cannot figure out if x= -6 or +6
because 4-10 is -6 could you please explain?
Sure! I can explain how to solve this equation algebraically.
To solve the equation x = √(x + 10) + 2, we need to isolate x on one side of the equation.
First, let's eliminate the square root (√) by squaring both sides of the equation:
(x)^2 = (√(x + 10) + 2)^2
Expanding the right side of the equation:
x^2 = (x + 10) + 4√(x + 10) + 4
Next, simplify and rearrange the equation:
x^2 = x + 14 + 4√(x + 10)
Now, we can isolate the root term by moving all the other terms to one side:
x^2 - x - 14 = 4√(x + 10)
To remove the square root, we need to square both sides of the equation again:
(x^2 - x - 14)^2 = (4√(x + 10))^2
Expanding the equation:
x^4 - 2x^3 - 15x^2 + 28x + 196 = 16(x + 10)
Simplifying further:
x^4 - 2x^3 - 15x^2 + 28x + 196 = 16x + 160
Now, let's bring everything to one side to solve for x:
x^4 - 2x^3 - 15x^2 + 28x + 196 - 16x - 160 = 0
Combining like terms:
x^4 - 2x^3 - 15x^2 + 12x + 36 = 0
The equation is now in the form of a quartic equation. To solve for x, you can use numerical methods such as factoring, the Rational Root Theorem, synthetic division, or a graphing calculator.
Please note that the solution to this equation may involve complex numbers or decimal approximations depending on the specific values of x.