# Solve Using the Square Root Property x^2+14x+11=0 x2+14x+11=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=14, and c=11 into the quadratic formula and solve for x.
-14±142-4⋅(1⋅11)2⋅1
Simplify.
Simplify the numerator.
Raise 14 to the power of 2.
x=-14±196-4⋅(1⋅11)2⋅1
Multiply 11 by 1.
x=-14±196-4⋅112⋅1
Multiply -4 by 11.
x=-14±196-442⋅1
Subtract 44 from 196.
x=-14±1522⋅1
Rewrite 152 as 22⋅38.
Factor 4 out of 152.
x=-14±4(38)2⋅1
Rewrite 4 as 22.
x=-14±22⋅382⋅1
x=-14±22⋅382⋅1
Pull terms out from under the radical.
x=-14±2382⋅1
x=-14±2382⋅1
Multiply 2 by 1.
x=-14±2382
Simplify -14±2382.
x=-7±38
x=-7±38
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 14 to the power of 2.
x=-14±196-4⋅(1⋅11)2⋅1
Multiply 11 by 1.
x=-14±196-4⋅112⋅1
Multiply -4 by 11.
x=-14±196-442⋅1
Subtract 44 from 196.
x=-14±1522⋅1
Rewrite 152 as 22⋅38.
Factor 4 out of 152.
x=-14±4(38)2⋅1
Rewrite 4 as 22.
x=-14±22⋅382⋅1
x=-14±22⋅382⋅1
Pull terms out from under the radical.
x=-14±2382⋅1
x=-14±2382⋅1
Multiply 2 by 1.
x=-14±2382
Simplify -14±2382.
x=-7±38
Change the ± to +.
x=-7+38
x=-7+38
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 14 to the power of 2.
x=-14±196-4⋅(1⋅11)2⋅1
Multiply 11 by 1.
x=-14±196-4⋅112⋅1
Multiply -4 by 11.
x=-14±196-442⋅1
Subtract 44 from 196.
x=-14±1522⋅1
Rewrite 152 as 22⋅38.
Factor 4 out of 152.
x=-14±4(38)2⋅1
Rewrite 4 as 22.
x=-14±22⋅382⋅1
x=-14±22⋅382⋅1
Pull terms out from under the radical.
x=-14±2382⋅1
x=-14±2382⋅1
Multiply 2 by 1.
x=-14±2382
Simplify -14±2382.
x=-7±38
Change the ± to -.
x=-7-38
x=-7-38
The final answer is the combination of both solutions.
x=-7+38,-7-38
The result can be shown in multiple forms.
Exact Form:
x=-7+38,-7-38
Decimal Form:
x=-0.83558599…,-13.16441400…
Solve Using the Square Root Property x^2+14x+11=0     