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Simplifying 576x2 + -1824x + 1369 = 0 Reorder the terms: 1369 + -1824x + 576x2 = 0 Solving 1369 + -1824x + 576x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 576 the coefficient of the squared term: Divide each side by '576'. 2.376736111 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '-2.376736111' to each side of the equation. 2.376736111 + -3.166666667x + -2.376736111 + x2 = 0 + -2.376736111 Reorder the terms: 2.376736111 + -2.376736111 + -3.166666667x + x2 = 0 + -2.376736111 Combine like terms: 2.376736111 + -2.376736111 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + -2.376736111 -3.166666667x + x2 = 0 + -2.376736111 Combine like terms: 0 + -2.376736111 = -2.376736111 -3.166666667x + x2 = -2.376736111 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = -2.376736111 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -2.376736111 + 2.506944447 Combine like terms: -2.376736111 + 2.506944447 = 0.130208336 2.506944447 + -3.166666667x + x2 = 0.130208336 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 0.130208336 Calculate the square root of the right side: 0.360843922 Break this problem into two subproblems by setting (x + -1.583333334) equal to 0.360843922 and -0.360843922.Subproblem 1
x + -1.583333334 = 0.360843922 Simplifying x + -1.583333334 = 0.360843922 Reorder the terms: -1.583333334 + x = 0.360843922 Solving -1.583333334 + x = 0.360843922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 0.360843922 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 0.360843922 + 1.583333334 x = 0.360843922 + 1.583333334 Combine like terms: 0.360843922 + 1.583333334 = 1.944177256 x = 1.944177256 Simplifying x = 1.944177256Subproblem 2
x + -1.583333334 = -0.360843922 Simplifying x + -1.583333334 = -0.360843922 Reorder the terms: -1.583333334 + x = -0.360843922 Solving -1.583333334 + x = -0.360843922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -0.360843922 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -0.360843922 + 1.583333334 x = -0.360843922 + 1.583333334 Combine like terms: -0.360843922 + 1.583333334 = 1.222489412 x = 1.222489412 Simplifying x = 1.222489412Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.944177256, 1.222489412}
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