Question

What is the solution to sqrt 17-x=x+3? Show your work.

Answer 1

Answer:

$x=1$

Step-by-step explanation:

Remember:

$(\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2$

Given the equation $\sqrt{17-x}=x+3$, you need to solve for the variable "x" to find its value.

You need to square both sides of the equation:

$(\sqrt{17-x})^2=(x+3)^2$

$17-x=(x+3)^2$

Simplifying, you get:

$17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0$

Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:

$(x-1)(x+8)=0$

Then:

$x_1=1\\x_2=-8$

Let's check if the first solution is correct:

$\sqrt{17-(1)}=(1)+3$

$4=4$ (It checks)

Let's check if the second solution is correct:

$\sqrt{17-(-8)}=(-8)+3$

$5\neq-5$ (It does not checks)

Therefore, the solution is:

$x=1$