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Simplifying 4x2 + -29x = -3x2 + -4 + -12 Reorder the terms: -29x + 4x2 = -3x2 + -4 + -12 Reorder the terms: -29x + 4x2 = -4 + -12 + -3x2 Combine like terms: -4 + -12 = -16 -29x + 4x2 = -16 + -3x2 Solving -29x + 4x2 = -16 + -3x2 Solving for variable 'x'. Reorder the terms: 16 + -29x + 4x2 + 3x2 = -16 + -3x2 + 16 + 3x2 Combine like terms: 4x2 + 3x2 = 7x2 16 + -29x + 7x2 = -16 + -3x2 + 16 + 3x2 Reorder the terms: 16 + -29x + 7x2 = -16 + 16 + -3x2 + 3x2 Combine like terms: -16 + 16 = 0 16 + -29x + 7x2 = 0 + -3x2 + 3x2 16 + -29x + 7x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 16 + -29x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.285714286 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '-2.285714286' to each side of the equation. 2.285714286 + -4.142857143x + -2.285714286 + x2 = 0 + -2.285714286 Reorder the terms: 2.285714286 + -2.285714286 + -4.142857143x + x2 = 0 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + -4.142857143x + x2 = 0 + -2.285714286 -4.142857143x + x2 = 0 + -2.285714286 Combine like terms: 0 + -2.285714286 = -2.285714286 -4.142857143x + x2 = -2.285714286 The x term is -4.142857143x. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143x + 4.290816329 + x2 = -2.285714286 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = -2.285714286 + 4.290816329 Combine like terms: -2.285714286 + 4.290816329 = 2.005102043 4.290816329 + -4.142857143x + x2 = 2.005102043 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 2.005102043 Calculate the square root of the right side: 1.416016258 Break this problem into two subproblems by setting (x + -2.071428572) equal to 1.416016258 and -1.416016258.Subproblem 1
x + -2.071428572 = 1.416016258 Simplifying x + -2.071428572 = 1.416016258 Reorder the terms: -2.071428572 + x = 1.416016258 Solving -2.071428572 + x = 1.416016258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = 1.416016258 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 1.416016258 + 2.071428572 x = 1.416016258 + 2.071428572 Combine like terms: 1.416016258 + 2.071428572 = 3.48744483 x = 3.48744483 Simplifying x = 3.48744483Subproblem 2
x + -2.071428572 = -1.416016258 Simplifying x + -2.071428572 = -1.416016258 Reorder the terms: -2.071428572 + x = -1.416016258 Solving -2.071428572 + x = -1.416016258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = -1.416016258 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -1.416016258 + 2.071428572 x = -1.416016258 + 2.071428572 Combine like terms: -1.416016258 + 2.071428572 = 0.655412314 x = 0.655412314 Simplifying x = 0.655412314Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.48744483, 0.655412314}
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