Solve Using the Square Root Property 6x^2-13x+6=0

Math
6×2-13x+6=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⋅6=36 and whose sum is b=-13.
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Factor -13 out of -13x.
6×2-13x+6=0
Rewrite -13 as -4 plus -9
6×2+(-4-9)x+6=0
Apply the distributive property.
6×2-4x-9x+6=0
6×2-4x-9x+6=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(6×2-4x)-9x+6=0
Factor out the greatest common factor (GCF) from each group.
2x(3x-2)-3(3x-2)=0
2x(3x-2)-3(3x-2)=0
Factor the polynomial by factoring out the greatest common factor, 3x-2.
(3x-2)(2x-3)=0
(3x-2)(2x-3)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
3x-2=0
2x-3=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
3x-2=0
Add 2 to both sides of the equation.
3x=2
Divide each term by 3 and simplify.
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Divide each term in 3x=2 by 3.
3×3=23
Cancel the common factor of 3.
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Cancel the common factor.
3×3=23
Divide x by 1.
x=23
x=23
x=23
x=23
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
2x-3=0
Add 3 to both sides of the equation.
2x=3
Divide each term by 2 and simplify.
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Divide each term in 2x=3 by 2.
2×2=32
Cancel the common factor of 2.
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Cancel the common factor.
2×2=32
Divide x by 1.
x=32
x=32
x=32
x=32
The final solution is all the values that make (3x-2)(2x-3)=0 true.
x=23,32
Solve Using the Square Root Property 6x^2-13x+6=0

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