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If using the method of completing the square to solve the quadratic equation x^2-18x-2=0x 2 −18x−2=0, which number would have to be added to "complete the square"?

Sagot :

The steps taken to complete the square is:

x² - 18x - 2 + 2= 0 + 2

x² - 18x = 2

x² - 18x + 81= 2 + 81

(x - 9)² = 83

x - 9 = ±√83

x = 9 + √83 or x = 9 - √83

A quadratic equation is a polynomial of degree 2. The standard form of a quadratic equation is given by:

ax² + bx + c = 0

Where a,b and c are constants

A quadratic equation always has two solutions.

Given the quadratic equation x² - 18x - 2 = 0, the steps below are used to solve the equation using completing the square method:

x² - 18x - 2 = 0

Add 2 to both sides

x² - 18x - 2 + 2= 0 + 2

x² - 18x = 2

Add to both sides the square of half of the coefficient of x (that is 81)

x² - 18x + 81= 2 + 81

(x - 9)² = 83

x - 9 = ±√83

x = 9 + √83 or x = 9 - √83

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