Kelly is designing a logo for a company. She creates the four-sided figure PBAC, as shown. Then, she creates an image of figure
PBAC by rotating it 90 degrees clockwise about point P to create
figure PB' A'C'. Then, she performs the same rotation to create
image PB''A''C'.

Solve for x over the real numbers:

x^2 - 10 x - 27 = 0

Hint: | Solve the quadratic equation by completing the square.

Add 27 to both sides:

x^2 - 10 x = 27

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 25 to both sides:

x^2 - 10 x + 25 = 52

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 5)^2 = 52

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 5 = 2 sqrt(13) or x - 5 = -2 sqrt(13)

Hint: | Look at the first equation: Solve for x.

Add 5 to both sides:

x = 5 + 2 sqrt(13) or x - 5 = -2 sqrt(13)

Hint: | Look at the second equation: Solve for x.

Add 5 to both sides:

x = 5 + 2√(13) or x = 5 - 2√(13)

the solution is h=10 because you add 9 to each side of the equation.