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Simplifying 4x2 + -18x + 11 = 0 Reorder the terms: 11 + -18x + 4x2 = 0 Solving 11 + -18x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -4.5x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -4.5x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -4.5x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -4.5x + x2 = 0 + -2.75 -4.5x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -4.5x + x2 = -2.75 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -2.75 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -2.75 + 5.0625 Combine like terms: -2.75 + 5.0625 = 2.3125 5.0625 + -4.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + -2.25) equal to 1.520690633 and -1.520690633.Subproblem 1
x + -2.25 = 1.520690633 Simplifying x + -2.25 = 1.520690633 Reorder the terms: -2.25 + x = 1.520690633 Solving -2.25 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.520690633 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.520690633 + 2.25 x = 1.520690633 + 2.25 Combine like terms: 1.520690633 + 2.25 = 3.770690633 x = 3.770690633 Simplifying x = 3.770690633Subproblem 2
x + -2.25 = -1.520690633 Simplifying x + -2.25 = -1.520690633 Reorder the terms: -2.25 + x = -1.520690633 Solving -2.25 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.520690633 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.520690633 + 2.25 x = -1.520690633 + 2.25 Combine like terms: -1.520690633 + 2.25 = 0.729309367 x = 0.729309367 Simplifying x = 0.729309367Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.770690633, 0.729309367}
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