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Simplifying 144x2 + 10x + -131 = 0 Reorder the terms: -131 + 10x + 144x2 = 0 Solving -131 + 10x + 144x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.9097222222 + 0.06944444444x + x2 = 0 Move the constant term to the right: Add '0.9097222222' to each side of the equation. -0.9097222222 + 0.06944444444x + 0.9097222222 + x2 = 0 + 0.9097222222 Reorder the terms: -0.9097222222 + 0.9097222222 + 0.06944444444x + x2 = 0 + 0.9097222222 Combine like terms: -0.9097222222 + 0.9097222222 = 0.0000000000 0.0000000000 + 0.06944444444x + x2 = 0 + 0.9097222222 0.06944444444x + x2 = 0 + 0.9097222222 Combine like terms: 0 + 0.9097222222 = 0.9097222222 0.06944444444x + x2 = 0.9097222222 The x term is 0.06944444444x. Take half its coefficient (0.03472222222). Square it (0.001205632716) and add it to both sides. Add '0.001205632716' to each side of the equation. 0.06944444444x + 0.001205632716 + x2 = 0.9097222222 + 0.001205632716 Reorder the terms: 0.001205632716 + 0.06944444444x + x2 = 0.9097222222 + 0.001205632716 Combine like terms: 0.9097222222 + 0.001205632716 = 0.910927854916 0.001205632716 + 0.06944444444x + x2 = 0.910927854916 Factor a perfect square on the left side: (x + 0.03472222222)(x + 0.03472222222) = 0.910927854916 Calculate the square root of the right side: 0.954425406 Break this problem into two subproblems by setting (x + 0.03472222222) equal to 0.954425406 and -0.954425406.Subproblem 1
x + 0.03472222222 = 0.954425406 Simplifying x + 0.03472222222 = 0.954425406 Reorder the terms: 0.03472222222 + x = 0.954425406 Solving 0.03472222222 + x = 0.954425406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03472222222' to each side of the equation. 0.03472222222 + -0.03472222222 + x = 0.954425406 + -0.03472222222 Combine like terms: 0.03472222222 + -0.03472222222 = 0.00000000000 0.00000000000 + x = 0.954425406 + -0.03472222222 x = 0.954425406 + -0.03472222222 Combine like terms: 0.954425406 + -0.03472222222 = 0.91970318378 x = 0.91970318378 Simplifying x = 0.91970318378Subproblem 2
x + 0.03472222222 = -0.954425406 Simplifying x + 0.03472222222 = -0.954425406 Reorder the terms: 0.03472222222 + x = -0.954425406 Solving 0.03472222222 + x = -0.954425406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03472222222' to each side of the equation. 0.03472222222 + -0.03472222222 + x = -0.954425406 + -0.03472222222 Combine like terms: 0.03472222222 + -0.03472222222 = 0.00000000000 0.00000000000 + x = -0.954425406 + -0.03472222222 x = -0.954425406 + -0.03472222222 Combine like terms: -0.954425406 + -0.03472222222 = -0.98914762822 x = -0.98914762822 Simplifying x = -0.98914762822Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.91970318378, -0.98914762822}
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