Solve Using the Square Root Property 4x^2-18x-52=0

Math
4×2-18x-52=0
Factor the left side of the equation.
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Factor 2 out of 4×2-18x-52.
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Factor 2 out of 4×2.
2(2×2)-18x-52=0
Factor 2 out of -18x.
2(2×2)+2(-9x)-52=0
Factor 2 out of -52.
2(2×2)+2(-9x)+2(-26)=0
Factor 2 out of 2(2×2)+2(-9x).
2(2×2-9x)+2(-26)=0
Factor 2 out of 2(2×2-9x)+2(-26).
2(2×2-9x-26)=0
2(2×2-9x-26)=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=2⋅-26=-52 and whose sum is b=-9.
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Factor -9 out of -9x.
2(2×2-9x-26)=0
Rewrite -9 as 4 plus -13
2(2×2+(4-13)x-26)=0
Apply the distributive property.
2(2×2+4x-13x-26)=0
2(2×2+4x-13x-26)=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
2((2×2+4x)-13x-26)=0
Factor out the greatest common factor (GCF) from each group.
2(2x(x+2)-13(x+2))=0
2(2x(x+2)-13(x+2))=0
Factor the polynomial by factoring out the greatest common factor, x+2.
2((x+2)(2x-13))=0
2((x+2)(2x-13))=0
Remove unnecessary parentheses.
2(x+2)(2x-13)=0
2(x+2)(2x-13)=0
2(x+2)(2x-13)=0
Divide each term by 2 and simplify.
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Divide each term in 2(x+2)(2x-13)=0 by 2.
2(x+2)(2x-13)2=02
Simplify 2(x+2)(2x-13)2.
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Cancel the common factor of 2.
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Cancel the common factor.
2(x+2)(2x-13)2=02
Divide (x+2)(2x-13) by 1.
(x+2)(2x-13)=02
(x+2)(2x-13)=02
Expand (x+2)(2x-13) using the FOIL Method.
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Apply the distributive property.
x(2x-13)+2(2x-13)=02
Apply the distributive property.
x(2x)+x⋅-13+2(2x-13)=02
Apply the distributive property.
x(2x)+x⋅-13+2(2x)+2⋅-13=02
x(2x)+x⋅-13+2(2x)+2⋅-13=02
Simplify and combine like terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
2x⋅x+x⋅-13+2(2x)+2⋅-13=02
Multiply x by x by adding the exponents.
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Move x.
2(x⋅x)+x⋅-13+2(2x)+2⋅-13=02
Multiply x by x.
2×2+x⋅-13+2(2x)+2⋅-13=02
2×2+x⋅-13+2(2x)+2⋅-13=02
Move -13 to the left of x.
2×2-13⋅x+2(2x)+2⋅-13=02
Multiply 2 by 2.
2×2-13x+4x+2⋅-13=02
Multiply 2 by -13.
2×2-13x+4x-26=02
2×2-13x+4x-26=02
Add -13x and 4x.
2×2-9x-26=02
2×2-9x-26=02
2×2-9x-26=02
Divide 0 by 2.
2×2-9x-26=0
2×2-9x-26=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=2⋅-26=-52 and whose sum is b=-9.
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Factor -9 out of -9x.
2×2-9x-26=0
Rewrite -9 as 4 plus -13
2×2+(4-13)x-26=0
Apply the distributive property.
2×2+4x-13x-26=0
2×2+4x-13x-26=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(2×2+4x)-13x-26=0
Factor out the greatest common factor (GCF) from each group.
2x(x+2)-13(x+2)=0
2x(x+2)-13(x+2)=0
Factor the polynomial by factoring out the greatest common factor, x+2.
(x+2)(2x-13)=0
(x+2)(2x-13)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x+2=0
2x-13=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
x+2=0
Subtract 2 from both sides of the equation.
x=-2
x=-2
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
2x-13=0
Add 13 to both sides of the equation.
2x=13
Divide each term by 2 and simplify.
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Divide each term in 2x=13 by 2.
2×2=132
Cancel the common factor of 2.
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Cancel the common factor.
2×2=132
Divide x by 1.
x=132
x=132
x=132
x=132
The final solution is all the values that make (x+2)(2x-13)=0 true.
x=-2,132
Solve Using the Square Root Property 4x^2-18x-52=0

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