Solve Using the Square Root Property 12=6x+x^2

Math
12=6x+x2
Rewrite the equation as 6x+x2=12.
6x+x2=12
Move 12 to the left side of the equation by subtracting it from both sides.
6x+x2-12=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=6, and c=-12 into the quadratic formula and solve for x.
-6±62-4⋅(1⋅-12)2⋅1
Simplify.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise 6 to the power of 2.
x=-6±36-4⋅(1⋅-12)2⋅1
Multiply -12 by 1.
x=-6±36-4⋅-122⋅1
Multiply -4 by -12.
x=-6±36+482⋅1
Add 36 and 48.
x=-6±842⋅1
Rewrite 84 as 22⋅21.
Tap for more steps…
Factor 4 out of 84.
x=-6±4(21)2⋅1
Rewrite 4 as 22.
x=-6±22⋅212⋅1
x=-6±22⋅212⋅1
Pull terms out from under the radical.
x=-6±2212⋅1
x=-6±2212⋅1
Multiply 2 by 1.
x=-6±2212
Simplify -6±2212.
x=-3±21
x=-3±21
Simplify the expression to solve for the + portion of the ±.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise 6 to the power of 2.
x=-6±36-4⋅(1⋅-12)2⋅1
Multiply -12 by 1.
x=-6±36-4⋅-122⋅1
Multiply -4 by -12.
x=-6±36+482⋅1
Add 36 and 48.
x=-6±842⋅1
Rewrite 84 as 22⋅21.
Tap for more steps…
Factor 4 out of 84.
x=-6±4(21)2⋅1
Rewrite 4 as 22.
x=-6±22⋅212⋅1
x=-6±22⋅212⋅1
Pull terms out from under the radical.
x=-6±2212⋅1
x=-6±2212⋅1
Multiply 2 by 1.
x=-6±2212
Simplify -6±2212.
x=-3±21
Change the ± to +.
x=-3+21
x=-3+21
Simplify the expression to solve for the – portion of the ±.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise 6 to the power of 2.
x=-6±36-4⋅(1⋅-12)2⋅1
Multiply -12 by 1.
x=-6±36-4⋅-122⋅1
Multiply -4 by -12.
x=-6±36+482⋅1
Add 36 and 48.
x=-6±842⋅1
Rewrite 84 as 22⋅21.
Tap for more steps…
Factor 4 out of 84.
x=-6±4(21)2⋅1
Rewrite 4 as 22.
x=-6±22⋅212⋅1
x=-6±22⋅212⋅1
Pull terms out from under the radical.
x=-6±2212⋅1
x=-6±2212⋅1
Multiply 2 by 1.
x=-6±2212
Simplify -6±2212.
x=-3±21
Change the ± to -.
x=-3-21
x=-3-21
The final answer is the combination of both solutions.
x=-3+21,-3-21
The result can be shown in multiple forms.
Exact Form:
x=-3+21,-3-21
Decimal Form:
x=1.58257569…,-7.58257569…
Solve Using the Square Root Property 12=6x+x^2

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top