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Simplifying 8 = 70x + 4.9x2 Solving 8 = 70x + 4.9x2 Solving for variable 'x'. Reorder the terms: 8 + -70x + -4.9x2 = 70x + -70x + 4.9x2 + -4.9x2 Combine like terms: 70x + -70x = 0 8 + -70x + -4.9x2 = 0 + 4.9x2 + -4.9x2 8 + -70x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 8 + -70x + -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'. -1.632653061 + 14.28571429x + x2 = 0 Move the constant term to the right: Add '1.632653061' to each side of the equation. -1.632653061 + 14.28571429x + 1.632653061 + x2 = 0 + 1.632653061 Reorder the terms: -1.632653061 + 1.632653061 + 14.28571429x + x2 = 0 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + 14.28571429x + x2 = 0 + 1.632653061 14.28571429x + x2 = 0 + 1.632653061 Combine like terms: 0 + 1.632653061 = 1.632653061 14.28571429x + x2 = 1.632653061 The x term is 14.28571429x. Take half its coefficient (7.142857145). Square it (51.02040819) and add it to both sides. Add '51.02040819' to each side of the equation. 14.28571429x + 51.02040819 + x2 = 1.632653061 + 51.02040819 Reorder the terms: 51.02040819 + 14.28571429x + x2 = 1.632653061 + 51.02040819 Combine like terms: 1.632653061 + 51.02040819 = 52.653061251 51.02040819 + 14.28571429x + x2 = 52.653061251 Factor a perfect square on the left side: (x + 7.142857145)(x + 7.142857145) = 52.653061251 Calculate the square root of the right side: 7.256242916 Break this problem into two subproblems by setting (x + 7.142857145) equal to 7.256242916 and -7.256242916.Subproblem 1
x + 7.142857145 = 7.256242916 Simplifying x + 7.142857145 = 7.256242916 Reorder the terms: 7.142857145 + x = 7.256242916 Solving 7.142857145 + x = 7.256242916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = 7.256242916 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = 7.256242916 + -7.142857145 x = 7.256242916 + -7.142857145 Combine like terms: 7.256242916 + -7.142857145 = 0.113385771 x = 0.113385771 Simplifying x = 0.113385771Subproblem 2
x + 7.142857145 = -7.256242916 Simplifying x + 7.142857145 = -7.256242916 Reorder the terms: 7.142857145 + x = -7.256242916 Solving 7.142857145 + x = -7.256242916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = -7.256242916 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = -7.256242916 + -7.142857145 x = -7.256242916 + -7.142857145 Combine like terms: -7.256242916 + -7.142857145 = -14.399100061 x = -14.399100061 Simplifying x = -14.399100061Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.113385771, -14.399100061}
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