Solve Using the Square Root Property 0=-16t^2+62t+4

Math
0=-16t2+62t+4
Rewrite the equation as -16t2+62t+4=0.
-16t2+62t+4=0
Factor -2 out of -16t2+62t+4.
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Factor -2 out of -16t2.
-2(8t2)+62t+4=0
Factor -2 out of 62t.
-2(8t2)-2(-31t)+4=0
Factor -2 out of 4.
-2(8t2)-2(-31t)-2⋅-2=0
Factor -2 out of -2(8t2)-2(-31t).
-2(8t2-31t)-2⋅-2=0
Factor -2 out of -2(8t2-31t)-2(-2).
-2(8t2-31t-2)=0
-2(8t2-31t-2)=0
Divide each term by -2 and simplify.
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Divide each term in -2(8t2-31t-2)=0 by -2.
-2(8t2-31t-2)-2=0-2
Cancel the common factor of -2.
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Cancel the common factor.
-2(8t2-31t-2)-2=0-2
Divide 8t2-31t-2 by 1.
8t2-31t-2=0-2
8t2-31t-2=0-2
Divide 0 by -2.
8t2-31t-2=0
8t2-31t-2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=8, b=-31, and c=-2 into the quadratic formula and solve for t.
31±(-31)2-4⋅(8⋅-2)2⋅8
Simplify.
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Simplify the numerator.
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Raise -31 to the power of 2.
t=31±961-4⋅(8⋅-2)2⋅8
Multiply 8 by -2.
t=31±961-4⋅-162⋅8
Multiply -4 by -16.
t=31±961+642⋅8
Add 961 and 64.
t=31±10252⋅8
Rewrite 1025 as 52⋅41.
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Factor 25 out of 1025.
t=31±25(41)2⋅8
Rewrite 25 as 52.
t=31±52⋅412⋅8
t=31±52⋅412⋅8
Pull terms out from under the radical.
t=31±5412⋅8
t=31±5412⋅8
Multiply 2 by 8.
t=31±54116
t=31±54116
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -31 to the power of 2.
t=31±961-4⋅(8⋅-2)2⋅8
Multiply 8 by -2.
t=31±961-4⋅-162⋅8
Multiply -4 by -16.
t=31±961+642⋅8
Add 961 and 64.
t=31±10252⋅8
Rewrite 1025 as 52⋅41.
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Factor 25 out of 1025.
t=31±25(41)2⋅8
Rewrite 25 as 52.
t=31±52⋅412⋅8
t=31±52⋅412⋅8
Pull terms out from under the radical.
t=31±5412⋅8
t=31±5412⋅8
Multiply 2 by 8.
t=31±54116
Change the ± to +.
t=31+54116
t=31+54116
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -31 to the power of 2.
t=31±961-4⋅(8⋅-2)2⋅8
Multiply 8 by -2.
t=31±961-4⋅-162⋅8
Multiply -4 by -16.
t=31±961+642⋅8
Add 961 and 64.
t=31±10252⋅8
Rewrite 1025 as 52⋅41.
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Factor 25 out of 1025.
t=31±25(41)2⋅8
Rewrite 25 as 52.
t=31±52⋅412⋅8
t=31±52⋅412⋅8
Pull terms out from under the radical.
t=31±5412⋅8
t=31±5412⋅8
Multiply 2 by 8.
t=31±54116
Change the ± to -.
t=31-54116
t=31-54116
The final answer is the combination of both solutions.
t=31+54116,31-54116
The result can be shown in multiple forms.
Exact Form:
t=31+54116,31-54116
Decimal Form:
t=3.93847632…,-0.06347632…
Solve Using the Square Root Property 0=-16t^2+62t+4

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