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Simplifying 0.268x2 + -2.601x + 3.792 = 0 Reorder the terms: 3.792 + -2.601x + 0.268x2 = 0 Solving 3.792 + -2.601x + 0.268x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.268 the coefficient of the squared term: Divide each side by '0.268'. 14.14925373 + -9.705223881x + x2 = 0 Move the constant term to the right: Add '-14.14925373' to each side of the equation. 14.14925373 + -9.705223881x + -14.14925373 + x2 = 0 + -14.14925373 Reorder the terms: 14.14925373 + -14.14925373 + -9.705223881x + x2 = 0 + -14.14925373 Combine like terms: 14.14925373 + -14.14925373 = 0.00000000 0.00000000 + -9.705223881x + x2 = 0 + -14.14925373 -9.705223881x + x2 = 0 + -14.14925373 Combine like terms: 0 + -14.14925373 = -14.14925373 -9.705223881x + x2 = -14.14925373 The x term is -9.705223881x. Take half its coefficient (-4.852611941). Square it (23.54784265) and add it to both sides. Add '23.54784265' to each side of the equation. -9.705223881x + 23.54784265 + x2 = -14.14925373 + 23.54784265 Reorder the terms: 23.54784265 + -9.705223881x + x2 = -14.14925373 + 23.54784265 Combine like terms: -14.14925373 + 23.54784265 = 9.39858892 23.54784265 + -9.705223881x + x2 = 9.39858892 Factor a perfect square on the left side: (x + -4.852611941)(x + -4.852611941) = 9.39858892 Calculate the square root of the right side: 3.065711813 Break this problem into two subproblems by setting (x + -4.852611941) equal to 3.065711813 and -3.065711813.Subproblem 1
x + -4.852611941 = 3.065711813 Simplifying x + -4.852611941 = 3.065711813 Reorder the terms: -4.852611941 + x = 3.065711813 Solving -4.852611941 + x = 3.065711813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.852611941' to each side of the equation. -4.852611941 + 4.852611941 + x = 3.065711813 + 4.852611941 Combine like terms: -4.852611941 + 4.852611941 = 0.000000000 0.000000000 + x = 3.065711813 + 4.852611941 x = 3.065711813 + 4.852611941 Combine like terms: 3.065711813 + 4.852611941 = 7.918323754 x = 7.918323754 Simplifying x = 7.918323754Subproblem 2
x + -4.852611941 = -3.065711813 Simplifying x + -4.852611941 = -3.065711813 Reorder the terms: -4.852611941 + x = -3.065711813 Solving -4.852611941 + x = -3.065711813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.852611941' to each side of the equation. -4.852611941 + 4.852611941 + x = -3.065711813 + 4.852611941 Combine like terms: -4.852611941 + 4.852611941 = 0.000000000 0.000000000 + x = -3.065711813 + 4.852611941 x = -3.065711813 + 4.852611941 Combine like terms: -3.065711813 + 4.852611941 = 1.786900128 x = 1.786900128 Simplifying x = 1.786900128Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.918323754, 1.786900128}
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