x2-10x+25=-9

Move 9 to the left side of the equation by adding it to both sides.

x2-10x+25+9=0

Add 25 and 9.

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 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 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 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