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Simplifying 24x2 + -19x + 3 = 0 Reorder the terms: 3 + -19x + 24x2 = 0 Solving 3 + -19x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.125 + -0.7916666667x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.7916666667x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.7916666667x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.7916666667x + x2 = 0 + -0.125 -0.7916666667x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.7916666667x + x2 = -0.125 The x term is -0.7916666667x. Take half its coefficient (-0.3958333334). Square it (0.1566840278) and add it to both sides. Add '0.1566840278' to each side of the equation. -0.7916666667x + 0.1566840278 + x2 = -0.125 + 0.1566840278 Reorder the terms: 0.1566840278 + -0.7916666667x + x2 = -0.125 + 0.1566840278 Combine like terms: -0.125 + 0.1566840278 = 0.0316840278 0.1566840278 + -0.7916666667x + x2 = 0.0316840278 Factor a perfect square on the left side: (x + -0.3958333334)(x + -0.3958333334) = 0.0316840278 Calculate the square root of the right side: 0.178000078 Break this problem into two subproblems by setting (x + -0.3958333334) equal to 0.178000078 and -0.178000078.Subproblem 1
x + -0.3958333334 = 0.178000078 Simplifying x + -0.3958333334 = 0.178000078 Reorder the terms: -0.3958333334 + x = 0.178000078 Solving -0.3958333334 + x = 0.178000078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3958333334' to each side of the equation. -0.3958333334 + 0.3958333334 + x = 0.178000078 + 0.3958333334 Combine like terms: -0.3958333334 + 0.3958333334 = 0.0000000000 0.0000000000 + x = 0.178000078 + 0.3958333334 x = 0.178000078 + 0.3958333334 Combine like terms: 0.178000078 + 0.3958333334 = 0.5738334114 x = 0.5738334114 Simplifying x = 0.5738334114Subproblem 2
x + -0.3958333334 = -0.178000078 Simplifying x + -0.3958333334 = -0.178000078 Reorder the terms: -0.3958333334 + x = -0.178000078 Solving -0.3958333334 + x = -0.178000078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3958333334' to each side of the equation. -0.3958333334 + 0.3958333334 + x = -0.178000078 + 0.3958333334 Combine like terms: -0.3958333334 + 0.3958333334 = 0.0000000000 0.0000000000 + x = -0.178000078 + 0.3958333334 x = -0.178000078 + 0.3958333334 Combine like terms: -0.178000078 + 0.3958333334 = 0.2178332554 x = 0.2178332554 Simplifying x = 0.2178332554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5738334114, 0.2178332554}
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