Solve the quadratic equation. $$\sqrt { x + 9 } = x + 7$$
A) The sum of the solutions is -13.
B) There is one negative solution and one extraneous root.
C) There is one positive solution and one extraneous root.
D) There are two positive solutions.
E) There are two negative solutions.

Question

Quizplus · Accepted Answer

Squaring both sides gives $x + 9 = (x + 7)^2$. Simplifying, we get $x + 9 = x^2 + 14x + 49$. Rearranging gives $x^2 + 13x + 40 = 0$. Solving this quadratic equation, we find roots $x = -5$ and $x = -8$. Checking these in the original equation, only $x = -5$ is valid, making $x = -8$ an extraneous root.

Solve the Quadratic Equation x+9=x+7\sqrt { x + 9 } = x + 7x+9​=x+7

Solve the Quadratic Equation $\sqrt { x + 9 } = x + 7$