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Simplifying (5x2 + -11x + 4) = 0 Reorder the terms: (4 + -11x + 5x2) = 0 Remove parenthesis around (4 + -11x + 5x2) 4 + -11x + 5x2 = 0 Solving 4 + -11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -2.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.2x + x2 = 0 + -0.8 -2.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.2x + x2 = -0.8 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 = -0.8 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -0.8 + 1.21 Combine like terms: -0.8 + 1.21 = 0.41 1.21 + -2.2x + x2 = 0.41 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + -1.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + -1.1 = 0.640312424 Simplifying x + -1.1 = 0.640312424 Reorder the terms: -1.1 + x = 0.640312424 Solving -1.1 + x = 0.640312424 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 = 0.640312424 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.640312424 + 1.1 x = 0.640312424 + 1.1 Combine like terms: 0.640312424 + 1.1 = 1.740312424 x = 1.740312424 Simplifying x = 1.740312424Subproblem 2
x + -1.1 = -0.640312424 Simplifying x + -1.1 = -0.640312424 Reorder the terms: -1.1 + x = -0.640312424 Solving -1.1 + x = -0.640312424 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 = -0.640312424 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.640312424 + 1.1 x = -0.640312424 + 1.1 Combine like terms: -0.640312424 + 1.1 = 0.459687576 x = 0.459687576 Simplifying x = 0.459687576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.740312424, 0.459687576}
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