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 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

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

Add 1 and 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