# Solve Using the Square Root Property 0=10x^2-502-2400 0=10×2-502-2400
Rewrite the equation as 10×2-502-2400=0.
10×2-502-2400=0
Subtract 2400 from -502.
10×2-2902=0
Add 2902 to both sides of the equation.
10×2=2902
Divide each term by 10 and simplify.
Divide each term in 10×2=2902 by 10.
10×210=290210
Cancel the common factor of 10.
Cancel the common factor.
10×210=290210
Divide x2 by 1.
x2=290210
x2=290210
Cancel the common factor of 2902 and 10.
Factor 2 out of 2902.
x2=2(1451)10
Cancel the common factors.
Factor 2 out of 10.
x2=2⋅14512⋅5
Cancel the common factor.
x2=2⋅14512⋅5
Rewrite the expression.
x2=14515
x2=14515
x2=14515
x2=14515
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x=±14515
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 14515 as 14515.
x=±14515
Multiply 14515 by 55.
x=±14515⋅55
Combine and simplify the denominator.
Multiply 14515 and 55.
x=±1451555
Raise 5 to the power of 1.
x=±1451555
Raise 5 to the power of 1.
x=±1451555
Use the power rule aman=am+n to combine exponents.
x=±1451551+1
x=±1451552
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
x=±14515(512)2
Apply the power rule and multiply exponents, (am)n=amn.
x=±14515512⋅2
Combine 12 and 2.
x=±14515522
Cancel the common factor of 2.
Cancel the common factor.
x=±14515522
Divide 1 by 1.
x=±145155
x=±145155
Evaluate the exponent.
x=±145155
x=±145155
x=±145155
Simplify the numerator.
Combine using the product rule for radicals.
x=±1451⋅55
Multiply 1451 by 5.
x=±72555
x=±72555
x=±72555
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=72555
Next, use the negative value of the ± to find the second solution.
x=-72555
The complete solution is the result of both the positive and negative portions of the solution.
x=72555,-72555
x=72555,-72555
x=72555,-72555
The result can be shown in multiple forms.
Exact Form:
x=72555,-72555
Decimal Form:
x=17.03525755…,-17.03525755…
Solve Using the Square Root Property 0=10x^2-502-2400     