Solve Using the Square Root Property 6x^2-11x-21=0

Math
6×2-11x-21=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⋅-21=-126 and whose sum is b=-11.
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Factor -11 out of -11x.
6×2-11x-21=0
Rewrite -11 as 7 plus -18
6×2+(7-18)x-21=0
Apply the distributive property.
6×2+7x-18x-21=0
6×2+7x-18x-21=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+7x)-18x-21=0
Factor out the greatest common factor (GCF) from each group.
x(6x+7)-3(6x+7)=0
x(6x+7)-3(6x+7)=0
Factor the polynomial by factoring out the greatest common factor, 6x+7.
(6x+7)(x-3)=0
(6x+7)(x-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.
6x+7=0
x-3=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
6x+7=0
Subtract 7 from both sides of the equation.
6x=-7
Divide each term by 6 and simplify.
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Divide each term in 6x=-7 by 6.
6×6=-76
Cancel the common factor of 6.
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Cancel the common factor.
6×6=-76
Divide x by 1.
x=-76
x=-76
Move the negative in front of the fraction.
x=-76
x=-76
x=-76
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
x-3=0
Add 3 to both sides of the equation.
x=3
x=3
The final solution is all the values that make (6x+7)(x-3)=0 true.
x=-76,3
Solve Using the Square Root Property 6x^2-11x-21=0

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