Solve using the Square Root Property (4t^2)/5=(3t)/5+27/10

Math
4t25=3t5+2710
Multiply both sides of the equation by 5.
4t2=3t5⋅(5)+2710⋅(5)
Simplify each term.
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Cancel the common factor of 5.
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Cancel the common factor.
4t2=3t5⋅5+2710⋅(5)
Rewrite the expression.
4t2=3t+2710⋅(5)
4t2=3t+2710⋅(5)
Cancel the common factor of 5.
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Factor 5 out of 10.
4t2=3t+275(2)⋅5
Cancel the common factor.
4t2=3t+275⋅2⋅5
Rewrite the expression.
4t2=3t+272
4t2=3t+272
4t2=3t+272
Subtract 3t from both sides of the equation.
4t2-3t=272
Move 272 to the left side of the equation by subtracting it from both sides.
4t2-3t-272=0
Multiply through by the least common denominator 2, then simplify.
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Apply the distributive property.
2(4t2)+2(-3t)+2(-272)=0
Simplify.
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Multiply 4 by 2.
8t2+2(-3t)+2(-272)=0
Multiply -3 by 2.
8t2-6t+2(-272)=0
Cancel the common factor of 2.
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Move the leading negative in -272 into the numerator.
8t2-6t+2(-272)=0
Cancel the common factor.
8t2-6t+2(-272)=0
Rewrite the expression.
8t2-6t-27=0
8t2-6t-27=0
8t2-6t-27=0
8t2-6t-27=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=8, b=-6, and c=-27 into the quadratic formula and solve for t.
6±(-6)2-4⋅(8⋅-27)2⋅8
Simplify.
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Simplify the numerator.
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Raise -6 to the power of 2.
t=6±36-4⋅(8⋅-27)2⋅8
Multiply 8 by -27.
t=6±36-4⋅-2162⋅8
Multiply -4 by -216.
t=6±36+8642⋅8
Add 36 and 864.
t=6±9002⋅8
Rewrite 900 as 302.
t=6±3022⋅8
Pull terms out from under the radical, assuming positive real numbers.
t=6±302⋅8
t=6±302⋅8
Multiply 2 by 8.
t=6±3016
Simplify 6±3016.
t=3±158
t=3±158
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -6 to the power of 2.
t=6±36-4⋅(8⋅-27)2⋅8
Multiply 8 by -27.
t=6±36-4⋅-2162⋅8
Multiply -4 by -216.
t=6±36+8642⋅8
Add 36 and 864.
t=6±9002⋅8
Rewrite 900 as 302.
t=6±3022⋅8
Pull terms out from under the radical, assuming positive real numbers.
t=6±302⋅8
t=6±302⋅8
Multiply 2 by 8.
t=6±3016
Simplify 6±3016.
t=3±158
Change the ± to +.
t=3+158
Add 3 and 15.
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 -6 to the power of 2.
t=6±36-4⋅(8⋅-27)2⋅8
Multiply 8 by -27.
t=6±36-4⋅-2162⋅8
Multiply -4 by -216.
t=6±36+8642⋅8
Add 36 and 864.
t=6±9002⋅8
Rewrite 900 as 302.
t=6±3022⋅8
Pull terms out from under the radical, assuming positive real numbers.
t=6±302⋅8
t=6±302⋅8
Multiply 2 by 8.
t=6±3016
Simplify 6±3016.
t=3±158
Change the ± to -.
t=3-158
Subtract 15 from 3.
t=-128
Cancel the common factor of -12 and 8.
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Factor 4 out of -12.
t=4(-3)8
Cancel the common factors.
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Factor 4 out of 8.
t=4⋅-34⋅2
Cancel the common factor.
t=4⋅-34⋅2
Rewrite the expression.
t=-32
t=-32
t=-32
Move the negative in front of the fraction.
t=-32
t=-32
The final answer is the combination of both solutions.
t=94,-32
Solve using the Square Root Property (4t^2)/5=(3t)/5+27/10

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