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Simplifying 2.5x2 + -5.5x + 2.3 = 0 Reorder the terms: 2.3 + -5.5x + 2.5x2 = 0 Solving 2.3 + -5.5x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 0.92 + -2.2x + x2 = 0 Move the constant term to the right: Add '-0.92' to each side of the equation. 0.92 + -2.2x + -0.92 + x2 = 0 + -0.92 Reorder the terms: 0.92 + -0.92 + -2.2x + x2 = 0 + -0.92 Combine like terms: 0.92 + -0.92 = 0.00 0.00 + -2.2x + x2 = 0 + -0.92 -2.2x + x2 = 0 + -0.92 Combine like terms: 0 + -0.92 = -0.92 -2.2x + x2 = -0.92 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -0.92 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -0.92 + 1.21 Combine like terms: -0.92 + 1.21 = 0.29 1.21 + -2.2x + x2 = 0.29 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (x + -1.1) equal to 0.538516481 and -0.538516481.Subproblem 1
x + -1.1 = 0.538516481 Simplifying x + -1.1 = 0.538516481 Reorder the terms: -1.1 + x = 0.538516481 Solving -1.1 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 0.538516481 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.538516481 + 1.1 x = 0.538516481 + 1.1 Combine like terms: 0.538516481 + 1.1 = 1.638516481 x = 1.638516481 Simplifying x = 1.638516481Subproblem 2
x + -1.1 = -0.538516481 Simplifying x + -1.1 = -0.538516481 Reorder the terms: -1.1 + x = -0.538516481 Solving -1.1 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -0.538516481 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.538516481 + 1.1 x = -0.538516481 + 1.1 Combine like terms: -0.538516481 + 1.1 = 0.561483519 x = 0.561483519 Simplifying x = 0.561483519Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.638516481, 0.561483519}
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