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Simplifying 0 = 10 + 35x + 4.9x2 Solving 0 = 10 + 35x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -35x + -4.9x2 = 10 + 35x + 4.9x2 + -10 + -35x + -4.9x2 Reorder the terms: -10 + -35x + -4.9x2 = 10 + -10 + 35x + -35x + 4.9x2 + -4.9x2 Combine like terms: 10 + -10 = 0 -10 + -35x + -4.9x2 = 0 + 35x + -35x + 4.9x2 + -4.9x2 -10 + -35x + -4.9x2 = 35x + -35x + 4.9x2 + -4.9x2 Combine like terms: 35x + -35x = 0 -10 + -35x + -4.9x2 = 0 + 4.9x2 + -4.9x2 -10 + -35x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 -10 + -35x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 2.040816327 + 7.142857143x + x2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + 7.142857143x + -2.040816327 + x2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + 7.142857143x + x2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + 7.142857143x + x2 = 0 + -2.040816327 7.142857143x + x2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 7.142857143x + x2 = -2.040816327 The x term is 7.142857143x. Take half its coefficient (3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. 7.142857143x + 12.75510204 + x2 = -2.040816327 + 12.75510204 Reorder the terms: 12.75510204 + 7.142857143x + x2 = -2.040816327 + 12.75510204 Combine like terms: -2.040816327 + 12.75510204 = 10.714285713 12.75510204 + 7.142857143x + x2 = 10.714285713 Factor a perfect square on the left side: (x + 3.571428572)(x + 3.571428572) = 10.714285713 Calculate the square root of the right side: 3.273268353 Break this problem into two subproblems by setting (x + 3.571428572) equal to 3.273268353 and -3.273268353.Subproblem 1
x + 3.571428572 = 3.273268353 Simplifying x + 3.571428572 = 3.273268353 Reorder the terms: 3.571428572 + x = 3.273268353 Solving 3.571428572 + x = 3.273268353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + x = 3.273268353 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + x = 3.273268353 + -3.571428572 x = 3.273268353 + -3.571428572 Combine like terms: 3.273268353 + -3.571428572 = -0.298160219 x = -0.298160219 Simplifying x = -0.298160219Subproblem 2
x + 3.571428572 = -3.273268353 Simplifying x + 3.571428572 = -3.273268353 Reorder the terms: 3.571428572 + x = -3.273268353 Solving 3.571428572 + x = -3.273268353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + x = -3.273268353 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + x = -3.273268353 + -3.571428572 x = -3.273268353 + -3.571428572 Combine like terms: -3.273268353 + -3.571428572 = -6.844696925 x = -6.844696925 Simplifying x = -6.844696925Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.298160219, -6.844696925}
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