Solve Using the Square Root Property 2x(4x+15)=27

Math
2x(4x+15)=27
Divide each term by 2 and simplify.
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Divide each term in 2x(4x+15)=27 by 2.
2x(4x+15)2=272
Simplify 2x(4x+15)2.
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Simplify terms.
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Cancel the common factor of 2.
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Cancel the common factor.
2x(4x+15)2=272
Divide x(4x+15) by 1.
x(4x+15)=272
x(4x+15)=272
Apply the distributive property.
x(4x)+x⋅15=272
Reorder.
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Rewrite using the commutative property of multiplication.
4x⋅x+x⋅15=272
Move 15 to the left of x.
4x⋅x+15⋅x=272
4x⋅x+15⋅x=272
4x⋅x+15⋅x=272
Multiply x by x by adding the exponents.
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Move x.
4(x⋅x)+15⋅x=272
Multiply x by x.
4×2+15⋅x=272
4×2+15x=272
4×2+15x=272
4×2+15x=272
Move 272 to the left side of the equation by subtracting it from both sides.
4×2+15x-272=0
Multiply through by the least common denominator 2, then simplify.
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Apply the distributive property.
2(4×2)+2(15x)+2(-272)=0
Simplify.
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Multiply 4 by 2.
8×2+2(15x)+2(-272)=0
Multiply 15 by 2.
8×2+30x+2(-272)=0
Cancel the common factor of 2.
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Move the leading negative in -272 into the numerator.
8×2+30x+2(-272)=0
Cancel the common factor.
8×2+30x+2(-272)=0
Rewrite the expression.
8×2+30x-27=0
8×2+30x-27=0
8×2+30x-27=0
8×2+30x-27=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=8, b=30, and c=-27 into the quadratic formula and solve for x.
-30±302-4⋅(8⋅-27)2⋅8
Simplify.
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Simplify the numerator.
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Raise 30 to the power of 2.
x=-30±900-4⋅(8⋅-27)2⋅8
Multiply 8 by -27.
x=-30±900-4⋅-2162⋅8
Multiply -4 by -216.
x=-30±900+8642⋅8
Add 900 and 864.
x=-30±17642⋅8
Rewrite 1764 as 422.
x=-30±4222⋅8
Pull terms out from under the radical, assuming positive real numbers.
x=-30±422⋅8
x=-30±422⋅8
Multiply 2 by 8.
x=-30±4216
Simplify -30±4216.
x=-15±218
x=-15±218
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise 30 to the power of 2.
x=-30±900-4⋅(8⋅-27)2⋅8
Multiply 8 by -27.
x=-30±900-4⋅-2162⋅8
Multiply -4 by -216.
x=-30±900+8642⋅8
Add 900 and 864.
x=-30±17642⋅8
Rewrite 1764 as 422.
x=-30±4222⋅8
Pull terms out from under the radical, assuming positive real numbers.
x=-30±422⋅8
x=-30±422⋅8
Multiply 2 by 8.
x=-30±4216
Simplify -30±4216.
x=-15±218
Change the ± to +.
x=-15+218
Add -15 and 21.
x=68
Cancel the common factor of 6 and 8.
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Factor 2 out of 6.
x=2(3)8
Cancel the common factors.
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Factor 2 out of 8.
x=2⋅32⋅4
Cancel the common factor.
x=2⋅32⋅4
Rewrite the expression.
x=34
x=34
x=34
x=34
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise 30 to the power of 2.
x=-30±900-4⋅(8⋅-27)2⋅8
Multiply 8 by -27.
x=-30±900-4⋅-2162⋅8
Multiply -4 by -216.
x=-30±900+8642⋅8
Add 900 and 864.
x=-30±17642⋅8
Rewrite 1764 as 422.
x=-30±4222⋅8
Pull terms out from under the radical, assuming positive real numbers.
x=-30±422⋅8
x=-30±422⋅8
Multiply 2 by 8.
x=-30±4216
Simplify -30±4216.
x=-15±218
Change the ± to -.
x=-15-218
Subtract 21 from -15.
x=-368
Cancel the common factor of -36 and 8.
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Factor 4 out of -36.
x=4(-9)8
Cancel the common factors.
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Factor 4 out of 8.
x=4⋅-94⋅2
Cancel the common factor.
x=4⋅-94⋅2
Rewrite the expression.
x=-92
x=-92
x=-92
Move the negative in front of the fraction.
x=-92
x=-92
The final answer is the combination of both solutions.
x=34,-92
Solve Using the Square Root Property 2x(4x+15)=27

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