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Solve the quadratic equations by completing the square.
x^2-4x=-1

User ZJorge
by
8.3k points

1 Answer

11 votes

Answer:

2 ± √3

Explanation:

Solving quadratic equation by completing squares:

x² - 4x = -1

  • Divide the coefficient of x by 2.

4 ÷ 2 = 2

  • Now, square the result and add that to both sides of the equation.

2² = 2* 2 = 4

x² - 4x + 4 = -1 + 4

x² - 4x + 4 = 3

x² - 2 * x * 2 + 2² = 3

  • Compare it with a² - 2ab + b² . Now , a = x and b = 2

(x - 2)² = 3

  • Take square root both sides

x - 2 = ±√3

x = 2 ± √3

Solutions: x = 2 +√3 ; 2 - √3

User Jephte
by
8.0k points

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