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Simplifying 0.939x2 + 190x + -144157 = 0 Reorder the terms: -144157 + 190x + 0.939x2 = 0 Solving -144157 + 190x + 0.939x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.939 the coefficient of the squared term: Divide each side by '0.939'. -153521.8317 + 202.342918x + x2 = 0 Move the constant term to the right: Add '153521.8317' to each side of the equation. -153521.8317 + 202.342918x + 153521.8317 + x2 = 0 + 153521.8317 Reorder the terms: -153521.8317 + 153521.8317 + 202.342918x + x2 = 0 + 153521.8317 Combine like terms: -153521.8317 + 153521.8317 = 0.0000 0.0000 + 202.342918x + x2 = 0 + 153521.8317 202.342918x + x2 = 0 + 153521.8317 Combine like terms: 0 + 153521.8317 = 153521.8317 202.342918x + x2 = 153521.8317 The x term is 202.342918x. Take half its coefficient (101.171459). Square it (10235.66412) and add it to both sides. Add '10235.66412' to each side of the equation. 202.342918x + 10235.66412 + x2 = 153521.8317 + 10235.66412 Reorder the terms: 10235.66412 + 202.342918x + x2 = 153521.8317 + 10235.66412 Combine like terms: 153521.8317 + 10235.66412 = 163757.49582 10235.66412 + 202.342918x + x2 = 163757.49582 Factor a perfect square on the left side: (x + 101.171459)(x + 101.171459) = 163757.49582 Calculate the square root of the right side: 404.669613166 Break this problem into two subproblems by setting (x + 101.171459) equal to 404.669613166 and -404.669613166.Subproblem 1
x + 101.171459 = 404.669613166 Simplifying x + 101.171459 = 404.669613166 Reorder the terms: 101.171459 + x = 404.669613166 Solving 101.171459 + x = 404.669613166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-101.171459' to each side of the equation. 101.171459 + -101.171459 + x = 404.669613166 + -101.171459 Combine like terms: 101.171459 + -101.171459 = 0.000000 0.000000 + x = 404.669613166 + -101.171459 x = 404.669613166 + -101.171459 Combine like terms: 404.669613166 + -101.171459 = 303.498154166 x = 303.498154166 Simplifying x = 303.498154166Subproblem 2
x + 101.171459 = -404.669613166 Simplifying x + 101.171459 = -404.669613166 Reorder the terms: 101.171459 + x = -404.669613166 Solving 101.171459 + x = -404.669613166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-101.171459' to each side of the equation. 101.171459 + -101.171459 + x = -404.669613166 + -101.171459 Combine like terms: 101.171459 + -101.171459 = 0.000000 0.000000 + x = -404.669613166 + -101.171459 x = -404.669613166 + -101.171459 Combine like terms: -404.669613166 + -101.171459 = -505.841072166 x = -505.841072166 Simplifying x = -505.841072166Solution
The solution to the problem is based on the solutions from the subproblems. x = {303.498154166, -505.841072166}
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