Questions: Solve: √(c+100)-c+10=0 c=

Solution Steps

To solve the equation \(\sqrt{c+100} - c + 10 = 0\), we can isolate the square root term and then square both sides to eliminate the square root. This will result in a quadratic equation in terms of \(c\), which we can solve using the quadratic formula or by factoring.

Starting with the equation: \[ \sqrt{c + 100} - c + 10 = 0 \] we can isolate the square root: \[ \sqrt{c + 100} = c - 10 \]

Next, we square both sides to eliminate the square root: \[ c + 100 = (c - 10)^2 \] Expanding the right side gives: \[ c + 100 = c^2 - 20c + 100 \]

Rearranging the equation leads to: \[ 0 = c^2 - 21c \] Factoring out \(c\) gives: \[ c(c - 21) = 0 \]

Setting each factor to zero, we find: \[ c = 0 \quad \text{or} \quad c = 21 \] Since we are looking for valid solutions, we check both values in the original equation. The valid solution is: \[ c = 21 \]

Final Answer