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

Math
0=-16t2+86-16
Rewrite the equation as -16t2+86-16=0.
-16t2+86-16=0
Simplify -16t2+86-16.
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Cancel the common factor of -16t2+86 and -16.
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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.
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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.
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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 by 8 and simplify.
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Divide each term in 8t2=43 by 8.
8t28=438
Cancel the common factor of 8.
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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
The complete solution is the result of both the positive and negative portions of the solution.
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Simplify the right side of the equation.
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Rewrite 438 as 438.
t=±438
Simplify the denominator.
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Rewrite 8 as 22⋅2.
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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.
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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.
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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.
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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.
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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.
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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

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