# Solve using the Square Root Property x^2-10x+25=-9

x2-10x+25=-9
Move all terms to the left side of the equation and simplify.
Move 9 to the left side of the equation by adding it to both sides.
x2-10x+25+9=0
x2-10x+34=0
x2-10x+34=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-10, and c=34 into the quadratic formula and solve for x.
10±(-10)2-4⋅(1⋅34)2⋅1
Simplify.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅34)2⋅1
Multiply 34 by 1.
x=10±100-4⋅342⋅1
Multiply -4 by 34.
x=10±100-1362⋅1
Subtract 136 from 100.
x=10±-362⋅1
Rewrite -36 as -1(36).
x=10±-1⋅362⋅1
Rewrite -1(36) as -1⋅36.
x=10±-1⋅362⋅1
Rewrite -1 as i.
x=10±i⋅362⋅1
Rewrite 36 as 62.
x=10±i⋅622⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=10±i⋅62⋅1
Move 6 to the left of i.
x=10±6i2⋅1
x=10±6i2⋅1
Multiply 2 by 1.
x=10±6i2
Simplify 10±6i2.
x=5±3i
x=5±3i
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⋅34)2⋅1
Multiply 34 by 1.
x=10±100-4⋅342⋅1
Multiply -4 by 34.
x=10±100-1362⋅1
Subtract 136 from 100.
x=10±-362⋅1
Rewrite -36 as -1(36).
x=10±-1⋅362⋅1
Rewrite -1(36) as -1⋅36.
x=10±-1⋅362⋅1
Rewrite -1 as i.
x=10±i⋅362⋅1
Rewrite 36 as 62.
x=10±i⋅622⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=10±i⋅62⋅1
Move 6 to the left of i.
x=10±6i2⋅1
x=10±6i2⋅1
Multiply 2 by 1.
x=10±6i2
Simplify 10±6i2.
x=5±3i
Change the ± to +.
x=5+3i
x=5+3i
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⋅34)2⋅1
Multiply 34 by 1.
x=10±100-4⋅342⋅1
Multiply -4 by 34.
x=10±100-1362⋅1
Subtract 136 from 100.
x=10±-362⋅1
Rewrite -36 as -1(36).
x=10±-1⋅362⋅1
Rewrite -1(36) as -1⋅36.
x=10±-1⋅362⋅1
Rewrite -1 as i.
x=10±i⋅362⋅1
Rewrite 36 as 62.
x=10±i⋅622⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=10±i⋅62⋅1
Move 6 to the left of i.
x=10±6i2⋅1
x=10±6i2⋅1
Multiply 2 by 1.
x=10±6i2
Simplify 10±6i2.
x=5±3i
Change the ± to -.
x=5-3i
x=5-3i
The final answer is the combination of both solutions.
x=5+3i,5-3i
Solve using the Square Root Property x^2-10x+25=-9

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