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 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 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 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