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Simplifying 7x2 + -34x + -24 = 0 Reorder the terms: -24 + -34x + 7x2 = 0 Solving -24 + -34x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -4.857142857x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -4.857142857x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -4.857142857x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -4.857142857x + x2 = 0 + 3.428571429 -4.857142857x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -4.857142857x + x2 = 3.428571429 The x term is -4.857142857x. Take half its coefficient (-2.428571429). Square it (5.897959186) and add it to both sides. Add '5.897959186' to each side of the equation. -4.857142857x + 5.897959186 + x2 = 3.428571429 + 5.897959186 Reorder the terms: 5.897959186 + -4.857142857x + x2 = 3.428571429 + 5.897959186 Combine like terms: 3.428571429 + 5.897959186 = 9.326530615 5.897959186 + -4.857142857x + x2 = 9.326530615 Factor a perfect square on the left side: (x + -2.428571429)(x + -2.428571429) = 9.326530615 Calculate the square root of the right side: 3.053936904 Break this problem into two subproblems by setting (x + -2.428571429) equal to 3.053936904 and -3.053936904.Subproblem 1
x + -2.428571429 = 3.053936904 Simplifying x + -2.428571429 = 3.053936904 Reorder the terms: -2.428571429 + x = 3.053936904 Solving -2.428571429 + x = 3.053936904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = 3.053936904 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = 3.053936904 + 2.428571429 x = 3.053936904 + 2.428571429 Combine like terms: 3.053936904 + 2.428571429 = 5.482508333 x = 5.482508333 Simplifying x = 5.482508333Subproblem 2
x + -2.428571429 = -3.053936904 Simplifying x + -2.428571429 = -3.053936904 Reorder the terms: -2.428571429 + x = -3.053936904 Solving -2.428571429 + x = -3.053936904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = -3.053936904 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = -3.053936904 + 2.428571429 x = -3.053936904 + 2.428571429 Combine like terms: -3.053936904 + 2.428571429 = -0.625365475 x = -0.625365475 Simplifying x = -0.625365475Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.482508333, -0.625365475}
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