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Simplifying 5x(5x) + 21x + 22 = 0 Remove parenthesis around (5x) 5x * 5x + 21x + 22 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + 21x + 22 = 0 Multiply 5 * 5 25x * x + 21x + 22 = 0 Multiply x * x 25x2 + 21x + 22 = 0 Reorder the terms: 22 + 21x + 25x2 = 0 Solving 22 + 21x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.88 + 0.84x + x2 = 0 Move the constant term to the right: Add '-0.88' to each side of the equation. 0.88 + 0.84x + -0.88 + x2 = 0 + -0.88 Reorder the terms: 0.88 + -0.88 + 0.84x + x2 = 0 + -0.88 Combine like terms: 0.88 + -0.88 = 0.00 0.00 + 0.84x + x2 = 0 + -0.88 0.84x + x2 = 0 + -0.88 Combine like terms: 0 + -0.88 = -0.88 0.84x + x2 = -0.88 The x term is 0.84x. Take half its coefficient (0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. 0.84x + 0.1764 + x2 = -0.88 + 0.1764 Reorder the terms: 0.1764 + 0.84x + x2 = -0.88 + 0.1764 Combine like terms: -0.88 + 0.1764 = -0.7036 0.1764 + 0.84x + x2 = -0.7036 Factor a perfect square on the left side: (x + 0.42)(x + 0.42) = -0.7036 Can't calculate square root of the right side. The solution to this equation could not be determined.
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