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Simplifying 29 + -8x = -7x(x + -3) Reorder the terms: 29 + -8x = -7x(-3 + x) 29 + -8x = (-3 * -7x + x * -7x) 29 + -8x = (21x + -7x2) Solving 29 + -8x = 21x + -7x2 Solving for variable 'x'. Combine like terms: -8x + -21x = -29x 29 + -29x + 7x2 = 21x + -7x2 + -21x + 7x2 Reorder the terms: 29 + -29x + 7x2 = 21x + -21x + -7x2 + 7x2 Combine like terms: 21x + -21x = 0 29 + -29x + 7x2 = 0 + -7x2 + 7x2 29 + -29x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 29 + -29x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.142857143 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '-4.142857143' to each side of the equation. 4.142857143 + -4.142857143x + -4.142857143 + x2 = 0 + -4.142857143 Reorder the terms: 4.142857143 + -4.142857143 + -4.142857143x + x2 = 0 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + -4.142857143x + x2 = 0 + -4.142857143 -4.142857143x + x2 = 0 + -4.142857143 Combine like terms: 0 + -4.142857143 = -4.142857143 -4.142857143x + x2 = -4.142857143 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 = -4.142857143 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = -4.142857143 + 4.290816329 Combine like terms: -4.142857143 + 4.290816329 = 0.147959186 4.290816329 + -4.142857143x + x2 = 0.147959186 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 0.147959186 Calculate the square root of the right side: 0.384654632 Break this problem into two subproblems by setting (x + -2.071428572) equal to 0.384654632 and -0.384654632.Subproblem 1
x + -2.071428572 = 0.384654632 Simplifying x + -2.071428572 = 0.384654632 Reorder the terms: -2.071428572 + x = 0.384654632 Solving -2.071428572 + x = 0.384654632 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 = 0.384654632 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 0.384654632 + 2.071428572 x = 0.384654632 + 2.071428572 Combine like terms: 0.384654632 + 2.071428572 = 2.456083204 x = 2.456083204 Simplifying x = 2.456083204Subproblem 2
x + -2.071428572 = -0.384654632 Simplifying x + -2.071428572 = -0.384654632 Reorder the terms: -2.071428572 + x = -0.384654632 Solving -2.071428572 + x = -0.384654632 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 = -0.384654632 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -0.384654632 + 2.071428572 x = -0.384654632 + 2.071428572 Combine like terms: -0.384654632 + 2.071428572 = 1.68677394 x = 1.68677394 Simplifying x = 1.68677394Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.456083204, 1.68677394}
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