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Simplifying 4x2 + -11x + 5 = 3x + 2 Reorder the terms: 5 + -11x + 4x2 = 3x + 2 Reorder the terms: 5 + -11x + 4x2 = 2 + 3x Solving 5 + -11x + 4x2 = 2 + 3x Solving for variable 'x'. Reorder the terms: 5 + -2 + -11x + -3x + 4x2 = 2 + 3x + -2 + -3x Combine like terms: 5 + -2 = 3 3 + -11x + -3x + 4x2 = 2 + 3x + -2 + -3x Combine like terms: -11x + -3x = -14x 3 + -14x + 4x2 = 2 + 3x + -2 + -3x Reorder the terms: 3 + -14x + 4x2 = 2 + -2 + 3x + -3x Combine like terms: 2 + -2 = 0 3 + -14x + 4x2 = 0 + 3x + -3x 3 + -14x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 3 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -3.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -3.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -3.5x + x2 = 0 + -0.75 -3.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -3.5x + x2 = -0.75 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -0.75 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.75 + 3.0625 Combine like terms: -0.75 + 3.0625 = 2.3125 3.0625 + -3.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + -1.75) equal to 1.520690633 and -1.520690633.Subproblem 1
x + -1.75 = 1.520690633 Simplifying x + -1.75 = 1.520690633 Reorder the terms: -1.75 + x = 1.520690633 Solving -1.75 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.520690633 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.520690633 + 1.75 x = 1.520690633 + 1.75 Combine like terms: 1.520690633 + 1.75 = 3.270690633 x = 3.270690633 Simplifying x = 3.270690633Subproblem 2
x + -1.75 = -1.520690633 Simplifying x + -1.75 = -1.520690633 Reorder the terms: -1.75 + x = -1.520690633 Solving -1.75 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.520690633 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.520690633 + 1.75 x = -1.520690633 + 1.75 Combine like terms: -1.520690633 + 1.75 = 0.229309367 x = 0.229309367 Simplifying x = 0.229309367Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.270690633, 0.229309367}
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