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Simplifying 4x2 + -37x + 81 = x Reorder the terms: 81 + -37x + 4x2 = x Solving 81 + -37x + 4x2 = x Solving for variable 'x'. Reorder the terms: 81 + -37x + -1x + 4x2 = x + -1x Combine like terms: -37x + -1x = -38x 81 + -38x + 4x2 = x + -1x Combine like terms: x + -1x = 0 81 + -38x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 20.25 + -9.5x + x2 = 0 Move the constant term to the right: Add '-20.25' to each side of the equation. 20.25 + -9.5x + -20.25 + x2 = 0 + -20.25 Reorder the terms: 20.25 + -20.25 + -9.5x + x2 = 0 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + -9.5x + x2 = 0 + -20.25 -9.5x + x2 = 0 + -20.25 Combine like terms: 0 + -20.25 = -20.25 -9.5x + x2 = -20.25 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -20.25 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -20.25 + 22.5625 Combine like terms: -20.25 + 22.5625 = 2.3125 22.5625 + -9.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + -4.75) equal to 1.520690633 and -1.520690633.Subproblem 1
x + -4.75 = 1.520690633 Simplifying x + -4.75 = 1.520690633 Reorder the terms: -4.75 + x = 1.520690633 Solving -4.75 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 1.520690633 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 1.520690633 + 4.75 x = 1.520690633 + 4.75 Combine like terms: 1.520690633 + 4.75 = 6.270690633 x = 6.270690633 Simplifying x = 6.270690633Subproblem 2
x + -4.75 = -1.520690633 Simplifying x + -4.75 = -1.520690633 Reorder the terms: -4.75 + x = -1.520690633 Solving -4.75 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -1.520690633 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -1.520690633 + 4.75 x = -1.520690633 + 4.75 Combine like terms: -1.520690633 + 4.75 = 3.229309367 x = 3.229309367 Simplifying x = 3.229309367Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.270690633, 3.229309367}
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