Solve Using the Square Root Property 3x^2=32-20x

Math
3×2=32-20x
Add 20x to both sides of the equation.
3×2+20x=32
Move 32 to the left side of the equation by subtracting it from both sides.
3×2+20x-32=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=3⋅-32=-96 and whose sum is b=20.
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Factor 20 out of 20x.
3×2+20(x)-32=0
Rewrite 20 as -4 plus 24
3×2+(-4+24)x-32=0
Apply the distributive property.
3×2-4x+24x-32=0
3×2-4x+24x-32=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(3×2-4x)+24x-32=0
Factor out the greatest common factor (GCF) from each group.
x(3x-4)+8(3x-4)=0
x(3x-4)+8(3x-4)=0
Factor the polynomial by factoring out the greatest common factor, 3x-4.
(3x-4)(x+8)=0
(3x-4)(x+8)=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-4=0
x+8=0
Set the first factor equal to 0 and solve.
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Set the first 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
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
x+8=0
Subtract 8 from both sides of the equation.
x=-8
x=-8
The final solution is all the values that make (3x-4)(x+8)=0 true.
x=43,-8
Solve Using the Square Root Property 3x^2=32-20x

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