Solve using the Square Root Property 144=(2x-2)(5+x)

Math
144=(2x-2)(5+x)
Rewrite the equation as (2x-2)(5+x)=144.
(2x-2)(5+x)=144
Simplify (2x-2)(5+x).
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Expand (2x-2)(5+x) using the FOIL Method.
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Apply the distributive property.
2x(5+x)-2(5+x)=144
Apply the distributive property.
2x⋅5+2x⋅x-2(5+x)=144
Apply the distributive property.
2x⋅5+2x⋅x-2⋅5-2x=144
2x⋅5+2x⋅x-2⋅5-2x=144
Simplify and combine like terms.
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Simplify each term.
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Multiply 5 by 2.
10x+2x⋅x-2⋅5-2x=144
Multiply x by x by adding the exponents.
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Move x.
10x+2(x⋅x)-2⋅5-2x=144
Multiply x by x.
10x+2×2-2⋅5-2x=144
10x+2×2-2⋅5-2x=144
Multiply -2 by 5.
10x+2×2-10-2x=144
10x+2×2-10-2x=144
Subtract 2x from 10x.
8x+2×2-10=144
8x+2×2-10=144
8x+2×2-10=144
Set the equation equal to zero.
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Move 144 to the left side of the equation by subtracting it from both sides.
8x+2×2-10-144=0
Subtract 144 from -10.
8x+2×2-154=0
8x+2×2-154=0
Factor the left side of the equation.
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Factor 2 out of 8x+2×2-154.
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Factor 2 out of 8x.
2(4x)+2×2-154
Factor 2 out of 2×2.
2(4x)+2(x2)-154
Factor 2 out of -154.
2(4x)+2×2+2⋅-77
Factor 2 out of 2(4x)+2×2.
2(4x+x2)+2⋅-77
Factor 2 out of 2(4x+x2)+2⋅-77.
2(4x+x2-77)
2(4x+x2-77)
Let u=x. Substitute u for all occurrences of x.
2(4u+u2-77)
Factor 4u+u2-77 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -77 and whose sum is 4.
-7,11
Write the factored form using these integers.
2((u-7)(u+11))
2((u-7)(u+11))
Factor.
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Replace all occurrences of u with x.
2((x-7)(x+11))
Remove unnecessary parentheses.
2(x-7)(x+11)
2(x-7)(x+11)
Replace the left side with the factored expression.
2(x-7)(x+11)=0
2(x-7)(x+11)=0
Divide each term in 2(x-7)(x+11)=0 by 2.
2(x-7)(x+11)2=02
Cancel the common factor of 2.
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Cancel the common factor.
2(x-7)(x+11)2=02
Divide (x-7)(x+11) by 1.
(x-7)(x+11)=02
(x-7)(x+11)=02
Divide 0 by 2.
(x-7)(x+11)=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
x+11=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.
x+11=0
Subtract 11 from both sides of the equation.
x=-11
x=-11
The final solution is all the values that make 2(x-7)(x+11)2=02 true.
x=7,-11
Solve using the Square Root Property 144=(2x-2)(5+x)

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