Solve Using the Square Root Property 120=(2x+1)(x+1)

Math
120=(2x+1)(x+1)
Rewrite the equation as (2x+1)(x+1)=120.
(2x+1)(x+1)=120
Simplify (2x+1)(x+1).
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Expand (2x+1)(x+1) using the FOIL Method.
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Apply the distributive property.
2x(x+1)+1(x+1)=120
Apply the distributive property.
2x⋅x+2x⋅1+1(x+1)=120
Apply the distributive property.
2x⋅x+2x⋅1+1x+1⋅1=120
2x⋅x+2x⋅1+1x+1⋅1=120
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x by adding the exponents.
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Move x.
2(x⋅x)+2x⋅1+1x+1⋅1=120
Multiply x by x.
2×2+2x⋅1+1x+1⋅1=120
2×2+2x⋅1+1x+1⋅1=120
Multiply 2 by 1.
2×2+2x+1x+1⋅1=120
Multiply x by 1.
2×2+2x+x+1⋅1=120
Multiply 1 by 1.
2×2+2x+x+1=120
2×2+2x+x+1=120
Add 2x and x.
2×2+3x+1=120
2×2+3x+1=120
2×2+3x+1=120
Move 120 to the left side of the equation by subtracting it from both sides.
2×2+3x+1-120=0
Subtract 120 from 1.
2×2+3x-119=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⋅-119=-238 and whose sum is b=3.
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Factor 3 out of 3x.
2×2+3(x)-119=0
Rewrite 3 as -14 plus 17
2×2+(-14+17)x-119=0
Apply the distributive property.
2×2-14x+17x-119=0
2×2-14x+17x-119=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(2×2-14x)+17x-119=0
Factor out the greatest common factor (GCF) from each group.
2x(x-7)+17(x-7)=0
2x(x-7)+17(x-7)=0
Factor the polynomial by factoring out the greatest common factor, x-7.
(x-7)(2x+17)=0
(x-7)(2x+17)=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-7=0
2x+17=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
x-7=0
Add 7 to both sides of the equation.
x=7
x=7
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
2x+17=0
Subtract 17 from both sides of the equation.
2x=-17
Divide each term by 2 and simplify.
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Divide each term in 2x=-17 by 2.
2×2=-172
Cancel the common factor of 2.
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Cancel the common factor.
2×2=-172
Divide x by 1.
x=-172
x=-172
Move the negative in front of the fraction.
x=-172
x=-172
x=-172
The final solution is all the values that make (x-7)(2x+17)=0 true.
x=7,-172
Solve Using the Square Root Property 120=(2x+1)(x+1)

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