Solve the following equation \$1 + x - \sqrt(5 - x) = 0\$.

Given equation

\$1 + x - \sqrt(5 - x) = 0\$

Subtract 1 + x from both sides to isolate the square root term and Multiply both sides by -1:

\$-\sqrt(5 - x) = -1 - x\$

\$\sqrt(5 - x) = 1 + x\$

Square both sides of the equation:

\$(\sqrt(5 - x))^2 = (1 + x)^2\$

\$(5 - x) = (1 + x)(1 + x)\$

\$5 - x = 1 + 2x + x^2\$

Move all terms to one side to set the equation to zero:

\$0 = x^2 + 2x + 1 + x - 5\$

\$0 = x^2 + 3x - 4\$

Factor the quadratic equation Set each factor equal to zero and solve for x:

0 = (x + 4)(x - 1)

x + 4 = 0
x = -4

x - 1 = 0
x = 1

Check both solutions in the original equation to ensure they are valid: For x = -4:

\$1 + (-4) - \sqrt(5 - (-4)) = 0\$

\$-3 - \sqrt(9) = 0\$

-6 = 0 (Invalid solution)

For x = 1:

\$1 + 1 - \sqrt(5 - 1) = 0\$

\$2 - \sqrt4 = 0\$

2 - 2 = 0

0 = 0 (Valid solution)

Therefore, the solution to the equation \$1 + x - \sqrt(5 - x) = 0 is x = 1\$.

This choice is not correct because the solution does not include both x=1 and x=4; it only contains one of these values

(x = 1, 4)

This choice is not correct because the solution does not include both x=2 and x=7; it only contains one of these values

(x = 2, 7)

This choice is correct because it correctly identifies that x=1 satisfies the equation \$1 + x - \sqrt(5 - x) = 0\$

x = 1

This choice is incorrect because the solution does not include x=−1 and x=−2; it only contains one of these values

(x = -1, -2)

Option

C

Can you summarize what you’ve understood in the above steps?