0=-16t2+86-16

Rewrite the equation as -16t2+86-16=0.

-16t2+86-16=0

Cancel the common factor of -16t2+86 and -16.

Factor 2 out of -16t2.

2(-8t2)+86-16=0

Factor 2 out of 86.

2(-8t2)+2(43)-16=0

Factor 2 out of 2(-8t2)+2(43).

2(-8t2+43)-16=0

Cancel the common factors.

Factor 2 out of -16.

2(-8t2+43)2(-8)=0

Cancel the common factor.

2(-8t2+43)2⋅-8=0

Rewrite the expression.

-8t2+43-8=0

-8t2+43-8=0

-8t2+43-8=0

Move the negative in front of the fraction.

–8t2+438=0

Factor -1 out of -8t2.

–(8t2)+438=0

Rewrite 43 as -1(-43).

–(8t2)-1(-43)8=0

Factor -1 out of -(8t2)-1(-43).

–(8t2-43)8=0

Simplify the expression.

Rewrite -(8t2-43) as -1(8t2-43).

–1(8t2-43)8=0

Move the negative in front of the fraction.

–8t2-438=0

Multiply -1 by -1.

18t2-438=0

Multiply 8t2-438 by 1.

8t2-438=0

8t2-438=0

8t2-438=0

Multiply both sides of the equation by 8.

8t2-43=0⋅(8)

Remove parentheses.

8t2-43=0⋅(8)

Multiply 0 by 8.

8t2-43=0

Add 43 to both sides of the equation.

8t2=43

Divide each term in 8t2=43 by 8.

8t28=438

Cancel the common factor of 8.

Cancel the common factor.

8t28=438

Divide t2 by 1.

t2=438

t2=438

t2=438

Take the square root of both sides of the equation to eliminate the exponent on the left side.

t=±438

Simplify the right side of the equation.

Rewrite 438 as 438.

t=±438

Simplify the denominator.

Rewrite 8 as 22⋅2.

Factor 4 out of 8.

t=±434(2)

Rewrite 4 as 22.

t=±4322⋅2

t=±4322⋅2

Pull terms out from under the radical.

t=±4322

t=±4322

Multiply 4322 by 22.

t=±4322⋅22

Combine and simplify the denominator.

Multiply 4322 and 22.

t=±432222

Move 2.

t=±4322(22)

Raise 2 to the power of 1.

t=±4322(22)

Raise 2 to the power of 1.

t=±4322(22)

Use the power rule aman=am+n to combine exponents.

t=±432221+1

Add 1 and 1.

t=±432222

Rewrite 22 as 2.

Use axn=axn to rewrite 2 as 212.

t=±4322(212)2

Apply the power rule and multiply exponents, (am)n=amn.

t=±4322⋅212⋅2

Combine 12 and 2.

t=±4322⋅222

Cancel the common factor of 2.

Cancel the common factor.

t=±4322⋅222

Divide 1 by 1.

t=±4322⋅2

t=±4322⋅2

Evaluate the exponent.

t=±4322⋅2

t=±4322⋅2

t=±4322⋅2

Simplify the numerator.

Combine using the product rule for radicals.

t=±43⋅22⋅2

Multiply 43 by 2.

t=±862⋅2

t=±862⋅2

Multiply 2 by 2.

t=±864

t=±864

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

t=864

Next, use the negative value of the ± to find the second solution.

t=-864

The complete solution is the result of both the positive and negative portions of the solution.

t=864,-864

t=864,-864

t=864,-864

The result can be shown in multiple forms.

Exact Form:

t=864,-864

Decimal Form:

t=2.31840462…,-2.31840462…

Solve using the Square Root Property 0=(-16t^2+86)/-16