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Simplifying 7x2 + 32x + -45 = 0 Reorder the terms: -45 + 32x + 7x2 = 0 Solving -45 + 32x + 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'. -6.428571429 + 4.571428571x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + 4.571428571x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + 4.571428571x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + 4.571428571x + x2 = 0 + 6.428571429 4.571428571x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 4.571428571x + x2 = 6.428571429 The x term is 4.571428571x. Take half its coefficient (2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. 4.571428571x + 5.224489797 + x2 = 6.428571429 + 5.224489797 Reorder the terms: 5.224489797 + 4.571428571x + x2 = 6.428571429 + 5.224489797 Combine like terms: 6.428571429 + 5.224489797 = 11.653061226 5.224489797 + 4.571428571x + x2 = 11.653061226 Factor a perfect square on the left side: (x + 2.285714286)(x + 2.285714286) = 11.653061226 Calculate the square root of the right side: 3.413658042 Break this problem into two subproblems by setting (x + 2.285714286) equal to 3.413658042 and -3.413658042.Subproblem 1
x + 2.285714286 = 3.413658042 Simplifying x + 2.285714286 = 3.413658042 Reorder the terms: 2.285714286 + x = 3.413658042 Solving 2.285714286 + x = 3.413658042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + x = 3.413658042 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + x = 3.413658042 + -2.285714286 x = 3.413658042 + -2.285714286 Combine like terms: 3.413658042 + -2.285714286 = 1.127943756 x = 1.127943756 Simplifying x = 1.127943756Subproblem 2
x + 2.285714286 = -3.413658042 Simplifying x + 2.285714286 = -3.413658042 Reorder the terms: 2.285714286 + x = -3.413658042 Solving 2.285714286 + x = -3.413658042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + x = -3.413658042 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + x = -3.413658042 + -2.285714286 x = -3.413658042 + -2.285714286 Combine like terms: -3.413658042 + -2.285714286 = -5.699372328 x = -5.699372328 Simplifying x = -5.699372328Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.127943756, -5.699372328}
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