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Simplifying 36x2 + 61x + -183 = 0 Reorder the terms: -183 + 61x + 36x2 = 0 Solving -183 + 61x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -5.083333333 + 1.694444444x + x2 = 0 Move the constant term to the right: Add '5.083333333' to each side of the equation. -5.083333333 + 1.694444444x + 5.083333333 + x2 = 0 + 5.083333333 Reorder the terms: -5.083333333 + 5.083333333 + 1.694444444x + x2 = 0 + 5.083333333 Combine like terms: -5.083333333 + 5.083333333 = 0.000000000 0.000000000 + 1.694444444x + x2 = 0 + 5.083333333 1.694444444x + x2 = 0 + 5.083333333 Combine like terms: 0 + 5.083333333 = 5.083333333 1.694444444x + x2 = 5.083333333 The x term is 1.694444444x. Take half its coefficient (0.847222222). Square it (0.7177854935) and add it to both sides. Add '0.7177854935' to each side of the equation. 1.694444444x + 0.7177854935 + x2 = 5.083333333 + 0.7177854935 Reorder the terms: 0.7177854935 + 1.694444444x + x2 = 5.083333333 + 0.7177854935 Combine like terms: 5.083333333 + 0.7177854935 = 5.8011188265 0.7177854935 + 1.694444444x + x2 = 5.8011188265 Factor a perfect square on the left side: (x + 0.847222222)(x + 0.847222222) = 5.8011188265 Calculate the square root of the right side: 2.408551188 Break this problem into two subproblems by setting (x + 0.847222222) equal to 2.408551188 and -2.408551188.Subproblem 1
x + 0.847222222 = 2.408551188 Simplifying x + 0.847222222 = 2.408551188 Reorder the terms: 0.847222222 + x = 2.408551188 Solving 0.847222222 + x = 2.408551188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.847222222' to each side of the equation. 0.847222222 + -0.847222222 + x = 2.408551188 + -0.847222222 Combine like terms: 0.847222222 + -0.847222222 = 0.000000000 0.000000000 + x = 2.408551188 + -0.847222222 x = 2.408551188 + -0.847222222 Combine like terms: 2.408551188 + -0.847222222 = 1.561328966 x = 1.561328966 Simplifying x = 1.561328966Subproblem 2
x + 0.847222222 = -2.408551188 Simplifying x + 0.847222222 = -2.408551188 Reorder the terms: 0.847222222 + x = -2.408551188 Solving 0.847222222 + x = -2.408551188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.847222222' to each side of the equation. 0.847222222 + -0.847222222 + x = -2.408551188 + -0.847222222 Combine like terms: 0.847222222 + -0.847222222 = 0.000000000 0.000000000 + x = -2.408551188 + -0.847222222 x = -2.408551188 + -0.847222222 Combine like terms: -2.408551188 + -0.847222222 = -3.25577341 x = -3.25577341 Simplifying x = -3.25577341Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.561328966, -3.25577341}
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