# Solve Using the Square Root Property x^2-10x+28=0

x2-10x+28=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-10, and c=28 into the quadratic formula and solve for x.
10±(-10)2-4⋅(1⋅28)2⋅1
Simplify.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅28)2⋅1
Multiply 28 by 1.
x=10±100-4⋅282⋅1
Multiply -4 by 28.
x=10±100-1122⋅1
Subtract 112 from 100.
x=10±-122⋅1
Rewrite -12 as -1(12).
x=10±-1⋅122⋅1
Rewrite -1(12) as -1⋅12.
x=10±-1⋅122⋅1
Rewrite -1 as i.
x=10±i⋅122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=10±i⋅4(3)2⋅1
Rewrite 4 as 22.
x=10±i⋅22⋅32⋅1
x=10±i⋅22⋅32⋅1
Pull terms out from under the radical.
x=10±i⋅(23)2⋅1
Move 2 to the left of i.
x=10±2i32⋅1
x=10±2i32⋅1
Multiply 2 by 1.
x=10±2i32
Simplify 10±2i32.
x=5±i3
x=5±i3
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⋅28)2⋅1
Multiply 28 by 1.
x=10±100-4⋅282⋅1
Multiply -4 by 28.
x=10±100-1122⋅1
Subtract 112 from 100.
x=10±-122⋅1
Rewrite -12 as -1(12).
x=10±-1⋅122⋅1
Rewrite -1(12) as -1⋅12.
x=10±-1⋅122⋅1
Rewrite -1 as i.
x=10±i⋅122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=10±i⋅4(3)2⋅1
Rewrite 4 as 22.
x=10±i⋅22⋅32⋅1
x=10±i⋅22⋅32⋅1
Pull terms out from under the radical.
x=10±i⋅(23)2⋅1
Move 2 to the left of i.
x=10±2i32⋅1
x=10±2i32⋅1
Multiply 2 by 1.
x=10±2i32
Simplify 10±2i32.
x=5±i3
Change the ± to +.
x=5+i3
x=5+i3
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⋅28)2⋅1
Multiply 28 by 1.
x=10±100-4⋅282⋅1
Multiply -4 by 28.
x=10±100-1122⋅1
Subtract 112 from 100.
x=10±-122⋅1
Rewrite -12 as -1(12).
x=10±-1⋅122⋅1
Rewrite -1(12) as -1⋅12.
x=10±-1⋅122⋅1
Rewrite -1 as i.
x=10±i⋅122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=10±i⋅4(3)2⋅1
Rewrite 4 as 22.
x=10±i⋅22⋅32⋅1
x=10±i⋅22⋅32⋅1
Pull terms out from under the radical.
x=10±i⋅(23)2⋅1
Move 2 to the left of i.
x=10±2i32⋅1
x=10±2i32⋅1
Multiply 2 by 1.
x=10±2i32
Simplify 10±2i32.
x=5±i3
Change the ± to -.
x=5-i3
x=5-i3
The final answer is the combination of both solutions.
x=5+i3,5-i3
Solve Using the Square Root Property x^2-10x+28=0