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Simplifying 7x2 + 2x = 37 + -32x Reorder the terms: 2x + 7x2 = 37 + -32x Solving 2x + 7x2 = 37 + -32x Solving for variable 'x'. Reorder the terms: -37 + 2x + 32x + 7x2 = 37 + -32x + -37 + 32x Combine like terms: 2x + 32x = 34x -37 + 34x + 7x2 = 37 + -32x + -37 + 32x Reorder the terms: -37 + 34x + 7x2 = 37 + -37 + -32x + 32x Combine like terms: 37 + -37 = 0 -37 + 34x + 7x2 = 0 + -32x + 32x -37 + 34x + 7x2 = -32x + 32x Combine like terms: -32x + 32x = 0 -37 + 34x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.285714286 + 4.857142857x + x2 = 0 Move the constant term to the right: Add '5.285714286' to each side of the equation. -5.285714286 + 4.857142857x + 5.285714286 + x2 = 0 + 5.285714286 Reorder the terms: -5.285714286 + 5.285714286 + 4.857142857x + x2 = 0 + 5.285714286 Combine like terms: -5.285714286 + 5.285714286 = 0.000000000 0.000000000 + 4.857142857x + x2 = 0 + 5.285714286 4.857142857x + x2 = 0 + 5.285714286 Combine like terms: 0 + 5.285714286 = 5.285714286 4.857142857x + x2 = 5.285714286 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 = 5.285714286 + 5.897959186 Reorder the terms: 5.897959186 + 4.857142857x + x2 = 5.285714286 + 5.897959186 Combine like terms: 5.285714286 + 5.897959186 = 11.183673472 5.897959186 + 4.857142857x + x2 = 11.183673472 Factor a perfect square on the left side: (x + 2.428571429)(x + 2.428571429) = 11.183673472 Calculate the square root of the right side: 3.344199975 Break this problem into two subproblems by setting (x + 2.428571429) equal to 3.344199975 and -3.344199975.Subproblem 1
x + 2.428571429 = 3.344199975 Simplifying x + 2.428571429 = 3.344199975 Reorder the terms: 2.428571429 + x = 3.344199975 Solving 2.428571429 + x = 3.344199975 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 = 3.344199975 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + x = 3.344199975 + -2.428571429 x = 3.344199975 + -2.428571429 Combine like terms: 3.344199975 + -2.428571429 = 0.915628546 x = 0.915628546 Simplifying x = 0.915628546Subproblem 2
x + 2.428571429 = -3.344199975 Simplifying x + 2.428571429 = -3.344199975 Reorder the terms: 2.428571429 + x = -3.344199975 Solving 2.428571429 + x = -3.344199975 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 = -3.344199975 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + x = -3.344199975 + -2.428571429 x = -3.344199975 + -2.428571429 Combine like terms: -3.344199975 + -2.428571429 = -5.772771404 x = -5.772771404 Simplifying x = -5.772771404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.915628546, -5.772771404}
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