can someone show me how to solve an equation algerbracially
x=sqrtx+10+2
x-sqrtx-12=0
let sqrtx=u
u^2-u-12=0
(u-4)(u+3)=0
u=4 or sqrt x=4 or x=16
u=-3 or sqrtx=-4 or x=16
sorry the equation should read x=sqrt(x+10)+2
To solve the equation algebraically, we need to isolate the variable x on one side of the equation. Let's go step by step:
1. Start by moving the terms that involve x to one side of the equation. In this case, we have the term √x on the right side, so we'll subtract it from both sides:
x - √x = 10 + 2
2. Now, we want to get rid of the square root on the left side. To do that, we can square both sides of the equation:
(x - √x)^2 = (10 + 2)^2
Squaring the left side eliminates the square root, and squaring the right side gives us (12)^2.
3. Expanding the squared term, we get:
(x - √x)(x - √x) = 144
4. Multiply the terms on the left side using the distributive property:
x^2 - 2√x * x + (√x)^2 = 144
Simplifying further:
x^2 - 2x√x + x = 144
5. Combine like terms:
x^2 - 2x√x + x - 144 = 0
Now we have a quadratic equation in terms of x. To continue solving, you can use factoring, completing the square, or the quadratic formula.