Solve Using the Square Root Property 18x^2-15x-12=0

Math
18×2-15x-12=0
Factor the left side of the equation.
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Factor 3 out of 18×2-15x-12.
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Factor 3 out of 18×2.
3(6×2)-15x-12=0
Factor 3 out of -15x.
3(6×2)+3(-5x)-12=0
Factor 3 out of -12.
3(6×2)+3(-5x)+3(-4)=0
Factor 3 out of 3(6×2)+3(-5x).
3(6×2-5x)+3(-4)=0
Factor 3 out of 3(6×2-5x)+3(-4).
3(6×2-5x-4)=0
3(6×2-5x-4)=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⋅-4=-24 and whose sum is b=-5.
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Factor -5 out of -5x.
3(6×2-5x-4)=0
Rewrite -5 as 3 plus -8
3(6×2+(3-8)x-4)=0
Apply the distributive property.
3(6×2+3x-8x-4)=0
3(6×2+3x-8x-4)=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
3((6×2+3x)-8x-4)=0
Factor out the greatest common factor (GCF) from each group.
3(3x(2x+1)-4(2x+1))=0
3(3x(2x+1)-4(2x+1))=0
Factor the polynomial by factoring out the greatest common factor, 2x+1.
3((2x+1)(3x-4))=0
3((2x+1)(3x-4))=0
Remove unnecessary parentheses.
3(2x+1)(3x-4)=0
3(2x+1)(3x-4)=0
3(2x+1)(3x-4)=0
Divide each term by 3 and simplify.
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Divide each term in 3(2x+1)(3x-4)=0 by 3.
3(2x+1)(3x-4)3=03
Simplify 3(2x+1)(3x-4)3.
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Cancel the common factor of 3.
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Cancel the common factor.
3(2x+1)(3x-4)3=03
Divide (2x+1)(3x-4) by 1.
(2x+1)(3x-4)=03
(2x+1)(3x-4)=03
Expand (2x+1)(3x-4) using the FOIL Method.
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Apply the distributive property.
2x(3x-4)+1(3x-4)=03
Apply the distributive property.
2x(3x)+2x⋅-4+1(3x-4)=03
Apply the distributive property.
2x(3x)+2x⋅-4+1(3x)+1⋅-4=03
2x(3x)+2x⋅-4+1(3x)+1⋅-4=03
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
2⋅3×2+2x⋅-4+1(3x)+1⋅-4=03
Multiply 2 by 3.
6×2+2x⋅-4+1(3x)+1⋅-4=03
Multiply -4 by 2.
6×2-8x+1(3x)+1⋅-4=03
Multiply 3x by 1.
6×2-8x+3x+1⋅-4=03
Multiply -4 by 1.
6×2-8x+3x-4=03
6×2-8x+3x-4=03
Add -8x and 3x.
6×2-5x-4=03
6×2-5x-4=03
6×2-5x-4=03
Divide 0 by 3.
6×2-5x-4=0
6×2-5x-4=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⋅-4=-24 and whose sum is b=-5.
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Factor -5 out of -5x.
6×2-5x-4=0
Rewrite -5 as 3 plus -8
6×2+(3-8)x-4=0
Apply the distributive property.
6×2+3x-8x-4=0
6×2+3x-8x-4=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+3x)-8x-4=0
Factor out the greatest common factor (GCF) from each group.
3x(2x+1)-4(2x+1)=0
3x(2x+1)-4(2x+1)=0
Factor the polynomial by factoring out the greatest common factor, 2x+1.
(2x+1)(3x-4)=0
(2x+1)(3x-4)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2x+1=0
3x-4=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
2x+1=0
Subtract 1 from both sides of the equation.
2x=-1
Divide each term by 2 and simplify.
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Divide each term in 2x=-1 by 2.
2×2=-12
Cancel the common factor of 2.
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Cancel the common factor.
2×2=-12
Divide x by 1.
x=-12
x=-12
Move the negative in front of the fraction.
x=-12
x=-12
x=-12
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
3x-4=0
Add 4 to both sides of the equation.
3x=4
Divide each term by 3 and simplify.
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Divide each term in 3x=4 by 3.
3×3=43
Cancel the common factor of 3.
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Cancel the common factor.
3×3=43
Divide x by 1.
x=43
x=43
x=43
x=43
The final solution is all the values that make (2x+1)(3x-4)=0 true.
x=-12,43
Solve Using the Square Root Property 18x^2-15x-12=0

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