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Simplifying 4.25x2 + -28x + 24 = 0 Reorder the terms: 24 + -28x + 4.25x2 = 0 Solving 24 + -28x + 4.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.25 the coefficient of the squared term: Divide each side by '4.25'. 5.647058824 + -6.588235294x + x2 = 0 Move the constant term to the right: Add '-5.647058824' to each side of the equation. 5.647058824 + -6.588235294x + -5.647058824 + x2 = 0 + -5.647058824 Reorder the terms: 5.647058824 + -5.647058824 + -6.588235294x + x2 = 0 + -5.647058824 Combine like terms: 5.647058824 + -5.647058824 = 0.000000000 0.000000000 + -6.588235294x + x2 = 0 + -5.647058824 -6.588235294x + x2 = 0 + -5.647058824 Combine like terms: 0 + -5.647058824 = -5.647058824 -6.588235294x + x2 = -5.647058824 The x term is -6.588235294x. Take half its coefficient (-3.294117647). Square it (10.85121107) and add it to both sides. Add '10.85121107' to each side of the equation. -6.588235294x + 10.85121107 + x2 = -5.647058824 + 10.85121107 Reorder the terms: 10.85121107 + -6.588235294x + x2 = -5.647058824 + 10.85121107 Combine like terms: -5.647058824 + 10.85121107 = 5.204152246 10.85121107 + -6.588235294x + x2 = 5.204152246 Factor a perfect square on the left side: (x + -3.294117647)(x + -3.294117647) = 5.204152246 Calculate the square root of the right side: 2.281261109 Break this problem into two subproblems by setting (x + -3.294117647) equal to 2.281261109 and -2.281261109.Subproblem 1
x + -3.294117647 = 2.281261109 Simplifying x + -3.294117647 = 2.281261109 Reorder the terms: -3.294117647 + x = 2.281261109 Solving -3.294117647 + x = 2.281261109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.294117647' to each side of the equation. -3.294117647 + 3.294117647 + x = 2.281261109 + 3.294117647 Combine like terms: -3.294117647 + 3.294117647 = 0.000000000 0.000000000 + x = 2.281261109 + 3.294117647 x = 2.281261109 + 3.294117647 Combine like terms: 2.281261109 + 3.294117647 = 5.575378756 x = 5.575378756 Simplifying x = 5.575378756Subproblem 2
x + -3.294117647 = -2.281261109 Simplifying x + -3.294117647 = -2.281261109 Reorder the terms: -3.294117647 + x = -2.281261109 Solving -3.294117647 + x = -2.281261109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.294117647' to each side of the equation. -3.294117647 + 3.294117647 + x = -2.281261109 + 3.294117647 Combine like terms: -3.294117647 + 3.294117647 = 0.000000000 0.000000000 + x = -2.281261109 + 3.294117647 x = -2.281261109 + 3.294117647 Combine like terms: -2.281261109 + 3.294117647 = 1.012856538 x = 1.012856538 Simplifying x = 1.012856538Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.575378756, 1.012856538}
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