Can someone EXPLAIN to me how to solve for x. Please don't just give me an answer because I won't learn anything from that.
sq root of (x+6) = x
(x+6)^.5 = x
multiply both sides by (x+6)^.5
(x+6) = x(x+6)^.5 but (x+6)^.5 is x
so
x+6 = x^2
x^2 - x - 6 = 0
(x-3)(x+2) - 0
so x = 3 or x=-2
try x = 3
sqrt(9) = 3 sure enough
try x = -2
sqrt (4) = -2 nope, negative root does not check
so x = 3 is the answer.
To solve for x in the equation √(x+6) = x, we'll need to follow a few steps:
Step 1: Square both sides of the equation to eliminate the square root.
(√(x+6))^2 = x^2
Step 2: Simplify the equation.
(x+6) = x^2
Step 3: Rearrange the equation to set it equal to zero.
x^2 - x - 6 = 0
Step 4: Factor the quadratic equation or use the quadratic formula to solve for x.
To factor, we need to find two numbers that multiply to -6 and add up to -1. Those numbers are -3 and 2.
(x-3)(x+2) = 0
So, either (x-3) = 0 or (x+2) = 0.
Solving these individually, we get:
x-3 = 0, which yields x = 3
x+2 = 0, which gives us x = -2
Thus, the solutions to the equation are x = 3 and x = -2.