x-1=(2-x)^(2) What are the solutions to the given equation? Choose 1 answer: (A) x=0 (B) x=(5-sqrt5)/(2) and x=(5+sqrt5)/(2) (C) x=(-1-sqrt21)/(2) and x=(-1+sqrt21)/(2) (D) The equation has no real solutions.

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x-1=(2-x)^(2) What are the solutions to the given equation? Choose 1 answer: (A)  x=0 (B)  x=(5-sqrt5)/(2) and  x=(5+sqrt5)/(2) (C)  x=(-1-sqrt21)/(2) and  x=(-1+sqrt21)/(2) (D) The equation has no real solutions.

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Expand equation: First, we need to expand the right side of the equation (2-x)². (2-x)² = (2-x)(2-x) = 4 - 4x + x²Rewrite equation: Now, we rewrite the original equation with the expanded form: x - 1 = 4 - 4x + x²Arrange equation: Next, we bring all terms to one side to set the equation to zero and arrange it in descending order of powers of x: x² - 4x + x - 4 + 1 = 0 x² - 3x - 3 = 0Quadratic formula: We now have a quadratic equation. To solve for x, we can use the quadratic formula x = [-b ± sqrt(b² - 4ac)] / (2a), where a = 1, b = -3, and c = -3.Solve using formula: Plugging the values into the quadratic formula: x = [-(-3) ± sqrt((-3)² - 4(1)(-3))] / (2(1)) x = [3 ± sqrt(9 + 12)] / 2 x = [3 ± sqrt(21)] / 2Simplify solution: Simplifying the square root and the expression: x = [3 ± sqrt(21)] / 2 So we have two solutions: x = (3 + sqrt(21)) / 2 x = (3 - sqrt(21)) / 2Compare solutions: We compare our solutions with the given options: (A) x=0 (Incorrect) (B) x=(5-sqrt5)/(2) and x=(5+sqrt5)/(2) (Incorrect) (C) x=(-1-sqrt21)/(2) and x=(-1+sqrt21)/(2) (Incorrect, sign error in the constant term) (D) The equation has no real solutions. (Incorrect, we found real solutions)

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