What are the solutions to this quadratic equation?

x2+13=8x+37

x = 4 + 2 sqrt(10) or x = 4 - 2 sqrt(10)

Step-by-step explanation:

Solve for x over the real numbers:

x^2 + 13 = 8 x + 37

Subtract 8 x + 37 from both sides:

x^2 - 8 x - 24 = 0

Add 24 to both sides:

x^2 - 8 x = 24

Add 16 to both sides:

x^2 - 8 x + 16 = 40

Write the left hand side as a square:

(x - 4)^2 = 40

Take the square root of both sides:

x - 4 = 2 sqrt(10) or x - 4 = -2 sqrt(10)

Add 4 to both sides:

x = 4 + 2 sqrt(10) or x - 4 = -2 sqrt(10)

Add 4 to both sides:

 x = 4 + 2 sqrt(10) or x = 4 - 2 sqrt(10)

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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hop i