-12×2-8x+71=0

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.

-(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 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 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 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