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Simplifying 3.25x2 + -12x = 9 Reorder the terms: -12x + 3.25x2 = 9 Solving -12x + 3.25x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -12x + 3.25x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -12x + 3.25x2 = 0 Begin completing the square. Divide all terms by 3.25 the coefficient of the squared term: Divide each side by '3.25'. -2.769230769 + -3.692307692x + x2 = 0 Move the constant term to the right: Add '2.769230769' to each side of the equation. -2.769230769 + -3.692307692x + 2.769230769 + x2 = 0 + 2.769230769 Reorder the terms: -2.769230769 + 2.769230769 + -3.692307692x + x2 = 0 + 2.769230769 Combine like terms: -2.769230769 + 2.769230769 = 0.000000000 0.000000000 + -3.692307692x + x2 = 0 + 2.769230769 -3.692307692x + x2 = 0 + 2.769230769 Combine like terms: 0 + 2.769230769 = 2.769230769 -3.692307692x + x2 = 2.769230769 The x term is -3.692307692x. Take half its coefficient (-1.846153846). Square it (3.408284023) and add it to both sides. Add '3.408284023' to each side of the equation. -3.692307692x + 3.408284023 + x2 = 2.769230769 + 3.408284023 Reorder the terms: 3.408284023 + -3.692307692x + x2 = 2.769230769 + 3.408284023 Combine like terms: 2.769230769 + 3.408284023 = 6.177514792 3.408284023 + -3.692307692x + x2 = 6.177514792 Factor a perfect square on the left side: (x + -1.846153846)(x + -1.846153846) = 6.177514792 Calculate the square root of the right side: 2.48546068 Break this problem into two subproblems by setting (x + -1.846153846) equal to 2.48546068 and -2.48546068.Subproblem 1
x + -1.846153846 = 2.48546068 Simplifying x + -1.846153846 = 2.48546068 Reorder the terms: -1.846153846 + x = 2.48546068 Solving -1.846153846 + x = 2.48546068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.846153846' to each side of the equation. -1.846153846 + 1.846153846 + x = 2.48546068 + 1.846153846 Combine like terms: -1.846153846 + 1.846153846 = 0.000000000 0.000000000 + x = 2.48546068 + 1.846153846 x = 2.48546068 + 1.846153846 Combine like terms: 2.48546068 + 1.846153846 = 4.331614526 x = 4.331614526 Simplifying x = 4.331614526Subproblem 2
x + -1.846153846 = -2.48546068 Simplifying x + -1.846153846 = -2.48546068 Reorder the terms: -1.846153846 + x = -2.48546068 Solving -1.846153846 + x = -2.48546068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.846153846' to each side of the equation. -1.846153846 + 1.846153846 + x = -2.48546068 + 1.846153846 Combine like terms: -1.846153846 + 1.846153846 = 0.000000000 0.000000000 + x = -2.48546068 + 1.846153846 x = -2.48546068 + 1.846153846 Combine like terms: -2.48546068 + 1.846153846 = -0.639306834 x = -0.639306834 Simplifying x = -0.639306834Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.331614526, -0.639306834}
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