Square root of 3-x=X+3 solve for x?

√ (3 - x) = x + 3 square both sides

(√ (3 - x)) ² = (x + 3) ²

3 - x = (x + 3) (x + 3)

3 - x = x (x + 3) + 3 (x + 3)

3 - x = x² + 3x + 3x + 9

3 - x = x² + 6x + 9

0 = x² + 6x + x + 9 - 3

0 = x² + 7x + 6

x² + 7x + 6 = 0 Solve the quadratic function. + 6 = + 6 * + 1

x² + x + 6x + 6 = 0

x (x + 1) + 6 (x + 1) = 0

(x+1) (x + 6) = 0

x + 1 = 0 or x + 6 = 0

x = 0 - 1, or x = 0 - 6, x = - 1, or - 6.

Check:

√ (3 - x) = x + 3 √ (3 - x) = x + 3

x = - 1 x = - 6

√ (3 - - 1) = - 1 + 3 √ (3 - - 6) = - 6 + 3

√ (3 + 1) = 3 - 1 √ (3 + 6) = 3 - 6

√4 = 3 - 1 √9 = - 3

2 = 2 Square root of 9 is also - 3,

LHS = RHS

Left Hand side (LHS) = Right Hand Side (RHS)

So the solutions x = - 1, and x = - 6 are correct for the surd equation.