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Simplifying 4.5x2 + -9x + 3.5 = 0 Reorder the terms: 3.5 + -9x + 4.5x2 = 0 Solving 3.5 + -9x + 4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. 0.7777777778 + -2x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -2x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -2x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.7777777778 -2x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -2x + x2 = -0.7777777778 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.7777777778 + 1 Reorder the terms: 1 + -2x + x2 = -0.7777777778 + 1 Combine like terms: -0.7777777778 + 1 = 0.2222222222 1 + -2x + x2 = 0.2222222222 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.2222222222 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (x + -1) equal to 0.471404521 and -0.471404521.Subproblem 1
x + -1 = 0.471404521 Simplifying x + -1 = 0.471404521 Reorder the terms: -1 + x = 0.471404521 Solving -1 + x = 0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.471404521 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.471404521 + 1 x = 0.471404521 + 1 Combine like terms: 0.471404521 + 1 = 1.471404521 x = 1.471404521 Simplifying x = 1.471404521Subproblem 2
x + -1 = -0.471404521 Simplifying x + -1 = -0.471404521 Reorder the terms: -1 + x = -0.471404521 Solving -1 + x = -0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.471404521 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.471404521 + 1 x = -0.471404521 + 1 Combine like terms: -0.471404521 + 1 = 0.528595479 x = 0.528595479 Simplifying x = 0.528595479Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.471404521, 0.528595479}
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