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Simplifying 83x2 + -145x + -130 = 0 Reorder the terms: -130 + -145x + 83x2 = 0 Solving -130 + -145x + 83x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 83 the coefficient of the squared term: Divide each side by '83'. -1.56626506 + -1.746987952x + x2 = 0 Move the constant term to the right: Add '1.56626506' to each side of the equation. -1.56626506 + -1.746987952x + 1.56626506 + x2 = 0 + 1.56626506 Reorder the terms: -1.56626506 + 1.56626506 + -1.746987952x + x2 = 0 + 1.56626506 Combine like terms: -1.56626506 + 1.56626506 = 0.00000000 0.00000000 + -1.746987952x + x2 = 0 + 1.56626506 -1.746987952x + x2 = 0 + 1.56626506 Combine like terms: 0 + 1.56626506 = 1.56626506 -1.746987952x + x2 = 1.56626506 The x term is -1.746987952x. Take half its coefficient (-0.873493976). Square it (0.7629917261) and add it to both sides. Add '0.7629917261' to each side of the equation. -1.746987952x + 0.7629917261 + x2 = 1.56626506 + 0.7629917261 Reorder the terms: 0.7629917261 + -1.746987952x + x2 = 1.56626506 + 0.7629917261 Combine like terms: 1.56626506 + 0.7629917261 = 2.3292567861 0.7629917261 + -1.746987952x + x2 = 2.3292567861 Factor a perfect square on the left side: (x + -0.873493976)(x + -0.873493976) = 2.3292567861 Calculate the square root of the right side: 1.526190285 Break this problem into two subproblems by setting (x + -0.873493976) equal to 1.526190285 and -1.526190285.Subproblem 1
x + -0.873493976 = 1.526190285 Simplifying x + -0.873493976 = 1.526190285 Reorder the terms: -0.873493976 + x = 1.526190285 Solving -0.873493976 + x = 1.526190285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.873493976' to each side of the equation. -0.873493976 + 0.873493976 + x = 1.526190285 + 0.873493976 Combine like terms: -0.873493976 + 0.873493976 = 0.000000000 0.000000000 + x = 1.526190285 + 0.873493976 x = 1.526190285 + 0.873493976 Combine like terms: 1.526190285 + 0.873493976 = 2.399684261 x = 2.399684261 Simplifying x = 2.399684261Subproblem 2
x + -0.873493976 = -1.526190285 Simplifying x + -0.873493976 = -1.526190285 Reorder the terms: -0.873493976 + x = -1.526190285 Solving -0.873493976 + x = -1.526190285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.873493976' to each side of the equation. -0.873493976 + 0.873493976 + x = -1.526190285 + 0.873493976 Combine like terms: -0.873493976 + 0.873493976 = 0.000000000 0.000000000 + x = -1.526190285 + 0.873493976 x = -1.526190285 + 0.873493976 Combine like terms: -1.526190285 + 0.873493976 = -0.652696309 x = -0.652696309 Simplifying x = -0.652696309Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.399684261, -0.652696309}
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