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Simplifying 0 = x2 + -24x + 0.44 Reorder the terms: 0 = 0.44 + -24x + x2 Solving 0 = 0.44 + -24x + x2 Solving for variable 'x'. Combine like terms: 0 + -0.44 = -0.44 -0.44 + 24x + -1x2 = 0.44 + -24x + x2 + -0.44 + 24x + -1x2 Reorder the terms: -0.44 + 24x + -1x2 = 0.44 + -0.44 + -24x + 24x + x2 + -1x2 Combine like terms: 0.44 + -0.44 = 0.00 -0.44 + 24x + -1x2 = 0.00 + -24x + 24x + x2 + -1x2 -0.44 + 24x + -1x2 = -24x + 24x + x2 + -1x2 Combine like terms: -24x + 24x = 0 -0.44 + 24x + -1x2 = 0 + x2 + -1x2 -0.44 + 24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -0.44 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.44 + -24x + x2 = 0 Move the constant term to the right: Add '-0.44' to each side of the equation. 0.44 + -24x + -0.44 + x2 = 0 + -0.44 Reorder the terms: 0.44 + -0.44 + -24x + x2 = 0 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 0.00 + -24x + x2 = 0 + -0.44 -24x + x2 = 0 + -0.44 Combine like terms: 0 + -0.44 = -0.44 -24x + x2 = -0.44 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -0.44 + 144 Reorder the terms: 144 + -24x + x2 = -0.44 + 144 Combine like terms: -0.44 + 144 = 143.56 144 + -24x + x2 = 143.56 Factor a perfect square on the left side: (x + -12)(x + -12) = 143.56 Calculate the square root of the right side: 11.981652641 Break this problem into two subproblems by setting (x + -12) equal to 11.981652641 and -11.981652641.Subproblem 1
x + -12 = 11.981652641 Simplifying x + -12 = 11.981652641 Reorder the terms: -12 + x = 11.981652641 Solving -12 + x = 11.981652641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.981652641 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.981652641 + 12 x = 11.981652641 + 12 Combine like terms: 11.981652641 + 12 = 23.981652641 x = 23.981652641 Simplifying x = 23.981652641Subproblem 2
x + -12 = -11.981652641 Simplifying x + -12 = -11.981652641 Reorder the terms: -12 + x = -11.981652641 Solving -12 + x = -11.981652641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.981652641 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.981652641 + 12 x = -11.981652641 + 12 Combine like terms: -11.981652641 + 12 = 0.018347359 x = 0.018347359 Simplifying x = 0.018347359Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.981652641, 0.018347359}
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