The solution of the quadratic equation x² - 2 · x = - 26 is x = 2 ± i √ 22.
Completing the square is an algebra-based method used both to simplify and to solve analytically quadratic equations. In this problem we proceed to complete the square to solve the equation, whose procedure is shown in detail:
x² - 2 · x = - 26 Given
x² - 2 · x + 4 = - 22 Compatibility with addition / Definition of subtraction
(x - 2)² = - 22 a² + 2 · a · b + b² = (a + b)²
x - 2 = ± √(- 22) Definition of square root
x - 2 = ± i √ 22 Definition of complex number
x = 2 ± i √ 22 Compatibility with addition / Existence of the additive inverse / Modulative property / Result
The solution of the quadratic equation x² - 2 · x = - 26 is x = 2 ± i √ 22.
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