Solve each equation

5 minus square root of 3-x =-2

1 answer

To solve the equation

\[ 5 - \sqrt{3 - x} = -2, \]

let's isolate the square root term:

  1. Subtract 5 from both sides:

\[ -\sqrt{3 - x} = -2 - 5, \] \[ -\sqrt{3 - x} = -7. \]

  1. Multiply both sides by -1:

\[ \sqrt{3 - x} = 7. \]

  1. Now, square both sides to eliminate the square root:

\[ 3 - x = 49. \]

  1. Rearranging gives:

\[ -x = 49 - 3, \] \[ -x = 46. \]

  1. Multiply both sides by -1 to solve for \( x \):

\[ x = -46. \]

Now, let’s check if this value satisfies the original equation:

Substituting \( x = -46 \) back into the original equation:

\[ 5 - \sqrt{3 - (-46)} = 5 - \sqrt{3 + 46} = 5 - \sqrt{49} = 5 - 7 = -2. \]

This is true!

Thus, the solution to the equation is

\[ \boxed{-46}. \]