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

Math
x2-10x+25=-28
Move all terms to the left side of the equation and simplify.
Tap for more steps…
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.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
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.
Tap for more steps…
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 ±.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
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.
Tap for more steps…
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 ±.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
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.
Tap for more steps…
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

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top