Solve using the Square Root Property 100=4.9t^2+8t

Math
100=4.9t2+8t
Rewrite the equation as 4.9t2+8t=100.
4.9t2+8t=100
Move 100 to the left side of the equation by subtracting it from both sides.
4.9t2+8t-100=0
Factor 0.1 out of 4.9t2+8t-100.
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Factor 0.1 out of 4.9t2.
0.1(49t2)+8t-100=0
Factor 0.1 out of 8t.
0.1(49t2)+0.1(80t)-100=0
Factor 0.1 out of -100.
0.1(49t2)+0.1(80t)+0.1(-1000)=0
Factor 0.1 out of 0.1(49t2)+0.1(80t).
0.1(49t2+80t)+0.1(-1000)=0
Factor 0.1 out of 0.1(49t2+80t)+0.1(-1000).
0.1(49t2+80t-1000)=0
0.1(49t2+80t-1000)=0
Divide each term by 0.1 and simplify.
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Divide each term in 0.1(49t2+80t-1000)=0 by 0.1.
0.1(49t2+80t-1000)0.1=00.1
Cancel the common factor of 0.1.
49t2+80t-1000=00.1
Divide 0 by 0.1.
49t2+80t-1000=0
49t2+80t-1000=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=49, b=80, and c=-1000 into the quadratic formula and solve for t.
-80±802-4⋅(49⋅-1000)2⋅49
Simplify.
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Simplify the numerator.
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Raise 80 to the power of 2.
t=-80±6400-4⋅(49⋅-1000)2⋅49
Multiply 49 by -1000.
t=-80±6400-4⋅-490002⋅49
Multiply -4 by -49000.
t=-80±6400+1960002⋅49
Add 6400 and 196000.
t=-80±2024002⋅49
Rewrite 202400 as 202⋅506.
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Factor 400 out of 202400.
t=-80±400(506)2⋅49
Rewrite 400 as 202.
t=-80±202⋅5062⋅49
t=-80±202⋅5062⋅49
Pull terms out from under the radical.
t=-80±205062⋅49
t=-80±205062⋅49
Multiply 2 by 49.
t=-80±2050698
Simplify -80±2050698.
t=-40±1050649
t=-40±1050649
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise 80 to the power of 2.
t=-80±6400-4⋅(49⋅-1000)2⋅49
Multiply 49 by -1000.
t=-80±6400-4⋅-490002⋅49
Multiply -4 by -49000.
t=-80±6400+1960002⋅49
Add 6400 and 196000.
t=-80±2024002⋅49
Rewrite 202400 as 202⋅506.
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Factor 400 out of 202400.
t=-80±400(506)2⋅49
Rewrite 400 as 202.
t=-80±202⋅5062⋅49
t=-80±202⋅5062⋅49
Pull terms out from under the radical.
t=-80±205062⋅49
t=-80±205062⋅49
Multiply 2 by 49.
t=-80±2050698
Simplify -80±2050698.
t=-40±1050649
Change the ± to +.
t=-40+1050649
Rewrite -40 as -1(40).
t=-1⋅40+1050649
Factor -1 out of 10506.
t=-1⋅40-(-10506)49
Factor -1 out of -1(40)-(-10506).
t=-1(40-10506)49
Move the negative in front of the fraction.
t=-40-1050649
t=-40-1050649
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise 80 to the power of 2.
t=-80±6400-4⋅(49⋅-1000)2⋅49
Multiply 49 by -1000.
t=-80±6400-4⋅-490002⋅49
Multiply -4 by -49000.
t=-80±6400+1960002⋅49
Add 6400 and 196000.
t=-80±2024002⋅49
Rewrite 202400 as 202⋅506.
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Factor 400 out of 202400.
t=-80±400(506)2⋅49
Rewrite 400 as 202.
t=-80±202⋅5062⋅49
t=-80±202⋅5062⋅49
Pull terms out from under the radical.
t=-80±205062⋅49
t=-80±205062⋅49
Multiply 2 by 49.
t=-80±2050698
Simplify -80±2050698.
t=-40±1050649
Change the ± to -.
t=-40-1050649
Rewrite -40 as -1(40).
t=-1⋅40-1050649
Factor -1 out of -10506.
t=-1⋅40-(10506)49
Factor -1 out of -1(40)-(10506).
t=-1(40+10506)49
Move the negative in front of the fraction.
t=-40+1050649
t=-40+1050649
The final answer is the combination of both solutions.
t=-40-1050649,-40+1050649
The result can be shown in multiple forms.
Exact Form:
t=-40-1050649,-40+1050649
Decimal Form:
t=3.77437627…,-5.40702933…
Solve using the Square Root Property 100=4.9t^2+8t

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