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Simplifying 7x2 = -29x + 24 Reorder the terms: 7x2 = 24 + -29x Solving 7x2 = 24 + -29x Solving for variable 'x'. Reorder the terms: -24 + 29x + 7x2 = 24 + -29x + -24 + 29x Reorder the terms: -24 + 29x + 7x2 = 24 + -24 + -29x + 29x Combine like terms: 24 + -24 = 0 -24 + 29x + 7x2 = 0 + -29x + 29x -24 + 29x + 7x2 = -29x + 29x Combine like terms: -29x + 29x = 0 -24 + 29x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + 4.142857143x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + 4.142857143x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + 4.142857143x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + 4.142857143x + x2 = 0 + 3.428571429 4.142857143x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 4.142857143x + x2 = 3.428571429 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 = 3.428571429 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143x + x2 = 3.428571429 + 4.290816329 Combine like terms: 3.428571429 + 4.290816329 = 7.719387758 4.290816329 + 4.142857143x + x2 = 7.719387758 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = 7.719387758 Calculate the square root of the right side: 2.77837862 Break this problem into two subproblems by setting (x + 2.071428572) equal to 2.77837862 and -2.77837862.Subproblem 1
x + 2.071428572 = 2.77837862 Simplifying x + 2.071428572 = 2.77837862 Reorder the terms: 2.071428572 + x = 2.77837862 Solving 2.071428572 + x = 2.77837862 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 = 2.77837862 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 2.77837862 + -2.071428572 x = 2.77837862 + -2.071428572 Combine like terms: 2.77837862 + -2.071428572 = 0.706950048 x = 0.706950048 Simplifying x = 0.706950048Subproblem 2
x + 2.071428572 = -2.77837862 Simplifying x + 2.071428572 = -2.77837862 Reorder the terms: 2.071428572 + x = -2.77837862 Solving 2.071428572 + x = -2.77837862 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 = -2.77837862 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -2.77837862 + -2.071428572 x = -2.77837862 + -2.071428572 Combine like terms: -2.77837862 + -2.071428572 = -4.849807192 x = -4.849807192 Simplifying x = -4.849807192Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.706950048, -4.849807192}
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