x2-10x+25=-28

Move 28 to the left side of the equation by adding it to both sides.

x2-10x+25+28=0

Add 25 and 28.

x2-10x+53=0

x2-10x+53=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-10, and c=53 into the quadratic formula and solve for x.

10±(-10)2-4⋅(1⋅53)2⋅1

Simplify the numerator.

Raise -10 to the power of 2.

x=10±100-4⋅(1⋅53)2⋅1

Multiply 53 by 1.

x=10±100-4⋅532⋅1

Multiply -4 by 53.

x=10±100-2122⋅1

Subtract 212 from 100.

x=10±-1122⋅1

Rewrite -112 as -1(112).

x=10±-1⋅1122⋅1

Rewrite -1(112) as -1⋅112.

x=10±-1⋅1122⋅1

Rewrite -1 as i.

x=10±i⋅1122⋅1

Rewrite 112 as 42⋅7.

Factor 16 out of 112.

x=10±i⋅16(7)2⋅1

Rewrite 16 as 42.

x=10±i⋅42⋅72⋅1

x=10±i⋅42⋅72⋅1

Pull terms out from under the radical.

x=10±i⋅(47)2⋅1

Move 4 to the left of i.

x=10±4i72⋅1

x=10±4i72⋅1

Multiply 2 by 1.

x=10±4i72

Simplify 10±4i72.

x=5±2i7

x=5±2i7

Simplify the numerator.

Raise -10 to the power of 2.

x=10±100-4⋅(1⋅53)2⋅1

Multiply 53 by 1.

x=10±100-4⋅532⋅1

Multiply -4 by 53.

x=10±100-2122⋅1

Subtract 212 from 100.

x=10±-1122⋅1

Rewrite -112 as -1(112).

x=10±-1⋅1122⋅1

Rewrite -1(112) as -1⋅112.

x=10±-1⋅1122⋅1

Rewrite -1 as i.

x=10±i⋅1122⋅1

Rewrite 112 as 42⋅7.

Factor 16 out of 112.

x=10±i⋅16(7)2⋅1

Rewrite 16 as 42.

x=10±i⋅42⋅72⋅1

x=10±i⋅42⋅72⋅1

Pull terms out from under the radical.

x=10±i⋅(47)2⋅1

Move 4 to the left of i.

x=10±4i72⋅1

x=10±4i72⋅1

Multiply 2 by 1.

x=10±4i72

Simplify 10±4i72.

x=5±2i7

Change the ± to +.

x=5+2i7

x=5+2i7

Simplify the numerator.

Raise -10 to the power of 2.

x=10±100-4⋅(1⋅53)2⋅1

Multiply 53 by 1.

x=10±100-4⋅532⋅1

Multiply -4 by 53.

x=10±100-2122⋅1

Subtract 212 from 100.

x=10±-1122⋅1

Rewrite -112 as -1(112).

x=10±-1⋅1122⋅1

Rewrite -1(112) as -1⋅112.

x=10±-1⋅1122⋅1

Rewrite -1 as i.

x=10±i⋅1122⋅1

Rewrite 112 as 42⋅7.

Factor 16 out of 112.

x=10±i⋅16(7)2⋅1

Rewrite 16 as 42.

x=10±i⋅42⋅72⋅1

x=10±i⋅42⋅72⋅1

Pull terms out from under the radical.

x=10±i⋅(47)2⋅1

Move 4 to the left of i.

x=10±4i72⋅1

x=10±4i72⋅1

Multiply 2 by 1.

x=10±4i72

Simplify 10±4i72.

x=5±2i7

Change the ± to -.

x=5-2i7

x=5-2i7

The final answer is the combination of both solutions.

x=5+2i7,5-2i7

Solve using the Square Root Property x^2-10x+25=-28