Solve Using the Square Root Property 24x^2+44x=8

Math
24×2+44x=8
Move 8 to the left side of the equation by subtracting it from both sides.
24×2+44x-8=0
Factor the left side of the equation.
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Factor 4 out of 24×2+44x-8.
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Factor 4 out of 24×2.
4(6×2)+44x-8=0
Factor 4 out of 44x.
4(6×2)+4(11x)-8=0
Factor 4 out of -8.
4(6×2)+4(11x)+4(-2)=0
Factor 4 out of 4(6×2)+4(11x).
4(6×2+11x)+4(-2)=0
Factor 4 out of 4(6×2+11x)+4(-2).
4(6×2+11x-2)=0
4(6×2+11x-2)=0
Factor.
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Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅-2=-12 and whose sum is b=11.
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Factor 11 out of 11x.
4(6×2+11(x)-2)=0
Rewrite 11 as -1 plus 12
4(6×2+(-1+12)x-2)=0
Apply the distributive property.
4(6×2-1x+12x-2)=0
4(6×2-1x+12x-2)=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
4((6×2-1x)+12x-2)=0
Factor out the greatest common factor (GCF) from each group.
4(x(6x-1)+2(6x-1))=0
4(x(6x-1)+2(6x-1))=0
Factor the polynomial by factoring out the greatest common factor, 6x-1.
4((6x-1)(x+2))=0
4((6x-1)(x+2))=0
Remove unnecessary parentheses.
4(6x-1)(x+2)=0
4(6x-1)(x+2)=0
4(6x-1)(x+2)=0
Divide each term by 4 and simplify.
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Divide each term in 4(6x-1)(x+2)=0 by 4.
4(6x-1)(x+2)4=04
Simplify 4(6x-1)(x+2)4.
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Cancel the common factor of 4.
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Cancel the common factor.
4(6x-1)(x+2)4=04
Divide (6x-1)(x+2) by 1.
(6x-1)(x+2)=04
(6x-1)(x+2)=04
Expand (6x-1)(x+2) using the FOIL Method.
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Apply the distributive property.
6x(x+2)-1(x+2)=04
Apply the distributive property.
6x⋅x+6x⋅2-1(x+2)=04
Apply the distributive property.
6x⋅x+6x⋅2-1x-1⋅2=04
6x⋅x+6x⋅2-1x-1⋅2=04
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x by adding the exponents.
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Move x.
6(x⋅x)+6x⋅2-1x-1⋅2=04
Multiply x by x.
6×2+6x⋅2-1x-1⋅2=04
6×2+6x⋅2-1x-1⋅2=04
Multiply 2 by 6.
6×2+12x-1x-1⋅2=04
Rewrite -1x as -x.
6×2+12x-x-1⋅2=04
Multiply -1 by 2.
6×2+12x-x-2=04
6×2+12x-x-2=04
Subtract x from 12x.
6×2+11x-2=04
6×2+11x-2=04
6×2+11x-2=04
Divide 0 by 4.
6×2+11x-2=0
6×2+11x-2=0
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅-2=-12 and whose sum is b=11.
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Factor 11 out of 11x.
6×2+11(x)-2=0
Rewrite 11 as -1 plus 12
6×2+(-1+12)x-2=0
Apply the distributive property.
6×2-1x+12x-2=0
6×2-1x+12x-2=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(6×2-1x)+12x-2=0
Factor out the greatest common factor (GCF) from each group.
x(6x-1)+2(6x-1)=0
x(6x-1)+2(6x-1)=0
Factor the polynomial by factoring out the greatest common factor, 6x-1.
(6x-1)(x+2)=0
(6x-1)(x+2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
6x-1=0
x+2=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
6x-1=0
Add 1 to both sides of the equation.
6x=1
Divide each term by 6 and simplify.
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Divide each term in 6x=1 by 6.
6×6=16
Cancel the common factor of 6.
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Cancel the common factor.
6×6=16
Divide x by 1.
x=16
x=16
x=16
x=16
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
x+2=0
Subtract 2 from both sides of the equation.
x=-2
x=-2
The final solution is all the values that make (6x-1)(x+2)=0 true.
x=16,-2
Solve Using the Square Root Property 24x^2+44x=8

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