# Solve Using the Square Root Property 17x+x^2=-52 17x+x2=-52
Move 52 to the left side of the equation by adding it to both sides.
17x+x2+52=0
Factor the left side of the equation.
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 and solve.
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 and solve.
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
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