# Solve using the Square Root Property x^2-10x+10=-5 x2-10x+10=-5
Move all terms to the left side of the equation and simplify.
Move 5 to the left side of the equation by adding it to both sides.
x2-10x+10+5=0
x2-10x+15=0
x2-10x+15=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-10, and c=15 into the quadratic formula and solve for x.
10±(-10)2-4⋅(1⋅15)2⋅1
Simplify.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅15)2⋅1
Multiply 15 by 1.
x=10±100-4⋅152⋅1
Multiply -4 by 15.
x=10±100-602⋅1
Subtract 60 from 100.
x=10±402⋅1
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
x=10±4(10)2⋅1
Rewrite 4 as 22.
x=10±22⋅102⋅1
x=10±22⋅102⋅1
Pull terms out from under the radical.
x=10±2102⋅1
x=10±2102⋅1
Multiply 2 by 1.
x=10±2102
Simplify 10±2102.
x=5±10
x=5±10
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅15)2⋅1
Multiply 15 by 1.
x=10±100-4⋅152⋅1
Multiply -4 by 15.
x=10±100-602⋅1
Subtract 60 from 100.
x=10±402⋅1
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
x=10±4(10)2⋅1
Rewrite 4 as 22.
x=10±22⋅102⋅1
x=10±22⋅102⋅1
Pull terms out from under the radical.
x=10±2102⋅1
x=10±2102⋅1
Multiply 2 by 1.
x=10±2102
Simplify 10±2102.
x=5±10
Change the ± to +.
x=5+10
x=5+10
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅15)2⋅1
Multiply 15 by 1.
x=10±100-4⋅152⋅1
Multiply -4 by 15.
x=10±100-602⋅1
Subtract 60 from 100.
x=10±402⋅1
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
x=10±4(10)2⋅1
Rewrite 4 as 22.
x=10±22⋅102⋅1
x=10±22⋅102⋅1
Pull terms out from under the radical.
x=10±2102⋅1
x=10±2102⋅1
Multiply 2 by 1.
x=10±2102
Simplify 10±2102.
x=5±10
Change the ± to -.
x=5-10
x=5-10
The final answer is the combination of both solutions.
x=5+10,5-10
The result can be shown in multiple forms.
Exact Form:
x=5+10,5-10
Decimal Form:
x=8.16227766…,1.83772233…
Solve using the Square Root Property x^2-10x+10=-5     