# Solve using the Square Root Property x^2-10x+25=-28 x2-10x+25=-28
Move all terms to the left side of the equation and simplify.
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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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   ## Download our App from the store

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