Solve Using the Square Root Property (4t^2)/5=(7t)/5+9/10

Math
4t25=7t5+910
Multiply both sides of the equation by 5.
4t2=7t5⋅(5)+910⋅(5)
Simplify each term.
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Cancel the common factor of 5.
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Cancel the common factor.
4t2=7t5⋅5+910⋅(5)
Rewrite the expression.
4t2=7t+910⋅(5)
4t2=7t+910⋅(5)
Cancel the common factor of 5.
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Factor 5 out of 10.
4t2=7t+95(2)⋅5
Cancel the common factor.
4t2=7t+95⋅2⋅5
Rewrite the expression.
4t2=7t+92
4t2=7t+92
4t2=7t+92
Subtract 7t from both sides of the equation.
4t2-7t=92
Move 92 to the left side of the equation by subtracting it from both sides.
4t2-7t-92=0
Multiply through by the least common denominator 2, then simplify.
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Apply the distributive property.
2(4t2)+2(-7t)+2(-92)=0
Simplify.
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Multiply 4 by 2.
8t2+2(-7t)+2(-92)=0
Multiply -7 by 2.
8t2-14t+2(-92)=0
Cancel the common factor of 2.
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Move the leading negative in -92 into the numerator.
8t2-14t+2(-92)=0
Cancel the common factor.
8t2-14t+2(-92)=0
Rewrite the expression.
8t2-14t-9=0
8t2-14t-9=0
8t2-14t-9=0
8t2-14t-9=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=8, b=-14, and c=-9 into the quadratic formula and solve for t.
14±(-14)2-4⋅(8⋅-9)2⋅8
Simplify.
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Simplify the numerator.
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Raise -14 to the power of 2.
t=14±196-4⋅(8⋅-9)2⋅8
Multiply 8 by -9.
t=14±196-4⋅-722⋅8
Multiply -4 by -72.
t=14±196+2882⋅8
Add 196 and 288.
t=14±4842⋅8
Rewrite 484 as 222.
t=14±2222⋅8
Pull terms out from under the radical, assuming positive real numbers.
t=14±222⋅8
t=14±222⋅8
Multiply 2 by 8.
t=14±2216
Simplify 14±2216.
t=7±118
t=7±118
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -14 to the power of 2.
t=14±196-4⋅(8⋅-9)2⋅8
Multiply 8 by -9.
t=14±196-4⋅-722⋅8
Multiply -4 by -72.
t=14±196+2882⋅8
Add 196 and 288.
t=14±4842⋅8
Rewrite 484 as 222.
t=14±2222⋅8
Pull terms out from under the radical, assuming positive real numbers.
t=14±222⋅8
t=14±222⋅8
Multiply 2 by 8.
t=14±2216
Simplify 14±2216.
t=7±118
Change the ± to +.
t=7+118
Add 7 and 11.
t=188
Cancel the common factor of 18 and 8.
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Factor 2 out of 18.
t=2(9)8
Cancel the common factors.
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Factor 2 out of 8.
t=2⋅92⋅4
Cancel the common factor.
t=2⋅92⋅4
Rewrite the expression.
t=94
t=94
t=94
t=94
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -14 to the power of 2.
t=14±196-4⋅(8⋅-9)2⋅8
Multiply 8 by -9.
t=14±196-4⋅-722⋅8
Multiply -4 by -72.
t=14±196+2882⋅8
Add 196 and 288.
t=14±4842⋅8
Rewrite 484 as 222.
t=14±2222⋅8
Pull terms out from under the radical, assuming positive real numbers.
t=14±222⋅8
t=14±222⋅8
Multiply 2 by 8.
t=14±2216
Simplify 14±2216.
t=7±118
Change the ± to -.
t=7-118
Subtract 11 from 7.
t=-48
Cancel the common factor of -4 and 8.
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Factor 4 out of -4.
t=4(-1)8
Cancel the common factors.
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Factor 4 out of 8.
t=4⋅-14⋅2
Cancel the common factor.
t=4⋅-14⋅2
Rewrite the expression.
t=-12
t=-12
t=-12
Move the negative in front of the fraction.
t=-12
t=-12
The final answer is the combination of both solutions.
t=94,-12
Solve Using the Square Root Property (4t^2)/5=(7t)/5+9/10

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