%5E2%2B25%3D0.jpeg "(x-9)^2+25=0")
Solving the Equation: (x - 9)² + 25 = 0
This equation presents a quadratic expression set equal to zero. We can solve for x using algebraic manipulation and understanding the properties of squares.
Steps to Solve
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Isolate the squared term: Subtract 25 from both sides of the equation. (x - 9)² = -25
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Take the square root of both sides: Remember that taking the square root introduces both positive and negative solutions. x - 9 = ±√(-25)
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Simplify the square root: The square root of -25 is an imaginary number, specifically 5i. x - 9 = ±5i
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Solve for x: Add 9 to both sides. x = 9 ± 5i
Solution
Therefore, the solutions to the equation (x - 9)² + 25 = 0 are:
- x = 9 + 5i
- x = 9 - 5i
Important Note: This equation has complex solutions because the square of a real number cannot be negative. The solutions involve the imaginary unit i, where i² = -1.