# Solve using the Square Root Property 23(x+5)^2+93=152

23(x+5)2+93=152
Subtract 93 from both sides of the equation.
23(x+5)2=152-93
Subtract 93 from 152.
23(x+5)2=59
Divide each term by 23 and simplify.
Divide each term in 23(x+5)2=59 by 23.
23(x+5)223=5923
Cancel the common factor of 23.
Cancel the common factor.
23(x+5)223=5923
Divide (x+5)2 by 1.
(x+5)2=5923
(x+5)2=5923
(x+5)2=5923
Take the square root of each side of the equation to set up the solution for x
(x+5)2⋅12=±5923
Remove the perfect root factor x+5 under the radical to solve for x.
x+5=±5923
Simplify the right side of the equation.
Rewrite 5923 as 5923.
x+5=±5923
Multiply 5923 by 2323.
x+5=±5923⋅2323
Combine and simplify the denominator.
Multiply 5923 and 2323.
x+5=±59232323
Raise 23 to the power of 1.
x+5=±59232323
Raise 23 to the power of 1.
x+5=±59232323
Use the power rule aman=am+n to combine exponents.
x+5=±5923231+1
Add 1 and 1.
x+5=±5923232
Rewrite 232 as 23.
Use axn=axn to rewrite 23 as 2312.
x+5=±5923(2312)2
Apply the power rule and multiply exponents, (am)n=amn.
x+5=±59232312⋅2
Combine 12 and 2.
x+5=±59232322
Cancel the common factor of 2.
Cancel the common factor.
x+5=±59232322
Divide 1 by 1.
x+5=±592323
x+5=±592323
Evaluate the exponent.
x+5=±592323
x+5=±592323
x+5=±592323
Simplify the numerator.
Combine using the product rule for radicals.
x+5=±59⋅2323
Multiply 59 by 23.
x+5=±135723
x+5=±135723
x+5=±135723
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
x+5=135723
Subtract 5 from both sides of the equation.
x=135723-5
Next, use the negative value of the ± to find the second solution.
x+5=-135723
Subtract 5 from both sides of the equation.
x=-135723-5
The complete solution is the result of both the positive and negative portions of the solution.
x=135723-5,-135723-5
x=135723-5,-135723-5
The result can be shown in multiple forms.
Exact Form:
x=135723-5,-135723-5
Decimal Form:
x=-3.39837039…,-6.60162960…
Solve using the Square Root Property 23(x+5)^2+93=152

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