# Solve Using the Square Root Property -12x^2-8x+71=0 -12×2-8x+71=0
Factor -1 out of -12×2-8x+71.
Factor -1 out of -12×2.
-(12×2)-8x+71=0
Factor -1 out of -8x.
-(12×2)-(8x)+71=0
Rewrite 71 as -1(-71).
-(12×2)-(8x)-1⋅-71=0
Factor -1 out of -(12×2)-(8x).
-(12×2+8x)-1⋅-71=0
Factor -1 out of -(12×2+8x)-1(-71).
-(12×2+8x-71)=0
-(12×2+8x-71)=0
Multiply each term in -(12×2+8x-71)=0 by -1
Multiply each term in -(12×2+8x-71)=0 by -1.
-(12×2+8x-71)⋅-1=0⋅-1
Simplify -(12×2+8x-71)⋅-1.
Apply the distributive property.
(-(12×2)-(8x)–71)⋅-1=0⋅-1
Simplify.
Multiply 12 by -1.
(-12×2-(8x)–71)⋅-1=0⋅-1
Multiply 8 by -1.
(-12×2-8x–71)⋅-1=0⋅-1
Multiply -1 by -71.
(-12×2-8x+71)⋅-1=0⋅-1
(-12×2-8x+71)⋅-1=0⋅-1
Apply the distributive property.
-12×2⋅-1-8x⋅-1+71⋅-1=0⋅-1
Simplify.
Multiply -1 by -12.
12×2-8x⋅-1+71⋅-1=0⋅-1
Multiply -1 by -8.
12×2+8x+71⋅-1=0⋅-1
Multiply 71 by -1.
12×2+8x-71=0⋅-1
12×2+8x-71=0⋅-1
12×2+8x-71=0⋅-1
Multiply 0 by -1.
12×2+8x-71=0
12×2+8x-71=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=12, b=8, and c=-71 into the quadratic formula and solve for x.
-8±82-4⋅(12⋅-71)2⋅12
Simplify.
Simplify the numerator.
Raise 8 to the power of 2.
x=-8±64-4⋅(12⋅-71)2⋅12
Multiply 12 by -71.
x=-8±64-4⋅-8522⋅12
Multiply -4 by -852.
x=-8±64+34082⋅12
Add 64 and 3408.
x=-8±34722⋅12
Rewrite 3472 as 42⋅217.
Factor 16 out of 3472.
x=-8±16(217)2⋅12
Rewrite 16 as 42.
x=-8±42⋅2172⋅12
x=-8±42⋅2172⋅12
Pull terms out from under the radical.
x=-8±42172⋅12
x=-8±42172⋅12
Multiply 2 by 12.
x=-8±421724
Simplify -8±421724.
x=-2±2176
x=-2±2176
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 8 to the power of 2.
x=-8±64-4⋅(12⋅-71)2⋅12
Multiply 12 by -71.
x=-8±64-4⋅-8522⋅12
Multiply -4 by -852.
x=-8±64+34082⋅12
Add 64 and 3408.
x=-8±34722⋅12
Rewrite 3472 as 42⋅217.
Factor 16 out of 3472.
x=-8±16(217)2⋅12
Rewrite 16 as 42.
x=-8±42⋅2172⋅12
x=-8±42⋅2172⋅12
Pull terms out from under the radical.
x=-8±42172⋅12
x=-8±42172⋅12
Multiply 2 by 12.
x=-8±421724
Simplify -8±421724.
x=-2±2176
Change the ± to +.
x=-2+2176
Rewrite -2 as -1(2).
x=-1⋅2+2176
Factor -1 out of 217.
x=-1⋅2-1(-217)6
Factor -1 out of -1(2)-1(-217).
x=-1(2-217)6
Move the negative in front of the fraction.
x=-2-2176
x=-2-2176
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 8 to the power of 2.
x=-8±64-4⋅(12⋅-71)2⋅12
Multiply 12 by -71.
x=-8±64-4⋅-8522⋅12
Multiply -4 by -852.
x=-8±64+34082⋅12
Add 64 and 3408.
x=-8±34722⋅12
Rewrite 3472 as 42⋅217.
Factor 16 out of 3472.
x=-8±16(217)2⋅12
Rewrite 16 as 42.
x=-8±42⋅2172⋅12
x=-8±42⋅2172⋅12
Pull terms out from under the radical.
x=-8±42172⋅12
x=-8±42172⋅12
Multiply 2 by 12.
x=-8±421724
Simplify -8±421724.
x=-2±2176
Change the ± to -.
x=-2-2176
Rewrite -2 as -1(2).
x=-1⋅2-2176
Factor -1 out of -217.
x=-1⋅2-(217)6
Factor -1 out of -1(2)-(217).
x=-1(2+217)6
Move the negative in front of the fraction.
x=-2+2176
x=-2+2176
The final answer is the combination of both solutions.
x=-2-2176,-2+2176
The result can be shown in multiple forms.
Exact Form:
x=-2-2176,-2+2176
Decimal Form:
x=2.12181997…,-2.78848664…
Solve Using the Square Root Property -12x^2-8x+71=0   ## Download our App from the store

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