17x+x2=-52

Move 52 to the left side of the equation by adding it to both sides.

17x+x2+52=0

Let u=x. Substitute u for all occurrences of x.

17u+u2+52

Factor 17u+u2+52 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 52 and whose sum is 17.

4,13

Write the factored form using these integers.

(u+4)(u+13)

(u+4)(u+13)

Replace all occurrences of u with x.

(x+4)(x+13)

Replace the left side with the factored expression.

(x+4)(x+13)=0

(x+4)(x+13)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x+4=0

x+13=0

Set the first factor equal to 0.

x+4=0

Subtract 4 from both sides of the equation.

x=-4

x=-4

Set the next factor equal to 0.

x+13=0

Subtract 13 from both sides of the equation.

x=-13

x=-13

The final solution is all the values that make (x+4)(x+13)=0 true.

x=-4,-13

Solve Using the Square Root Property 17x+x^2=-52