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Simplifying (2x2 + 6x + -5) = 85(x2 + 1) Reorder the terms: (-5 + 6x + 2x2) = 85(x2 + 1) Remove parenthesis around (-5 + 6x + 2x2) -5 + 6x + 2x2 = 85(x2 + 1) Reorder the terms: -5 + 6x + 2x2 = 85(1 + x2) -5 + 6x + 2x2 = (1 * 85 + x2 * 85) -5 + 6x + 2x2 = (85 + 85x2) Solving -5 + 6x + 2x2 = 85 + 85x2 Solving for variable 'x'. Reorder the terms: -5 + -85 + 6x + 2x2 + -85x2 = 85 + 85x2 + -85 + -85x2 Combine like terms: -5 + -85 = -90 -90 + 6x + 2x2 + -85x2 = 85 + 85x2 + -85 + -85x2 Combine like terms: 2x2 + -85x2 = -83x2 -90 + 6x + -83x2 = 85 + 85x2 + -85 + -85x2 Reorder the terms: -90 + 6x + -83x2 = 85 + -85 + 85x2 + -85x2 Combine like terms: 85 + -85 = 0 -90 + 6x + -83x2 = 0 + 85x2 + -85x2 -90 + 6x + -83x2 = 85x2 + -85x2 Combine like terms: 85x2 + -85x2 = 0 -90 + 6x + -83x2 = 0 Begin completing the square. Divide all terms by -83 the coefficient of the squared term: Divide each side by '-83'. 1.084337349 + -0.07228915663x + x2 = 0 Move the constant term to the right: Add '-1.084337349' to each side of the equation. 1.084337349 + -0.07228915663x + -1.084337349 + x2 = 0 + -1.084337349 Reorder the terms: 1.084337349 + -1.084337349 + -0.07228915663x + x2 = 0 + -1.084337349 Combine like terms: 1.084337349 + -1.084337349 = 0.000000000 0.000000000 + -0.07228915663x + x2 = 0 + -1.084337349 -0.07228915663x + x2 = 0 + -1.084337349 Combine like terms: 0 + -1.084337349 = -1.084337349 -0.07228915663x + x2 = -1.084337349 The x term is -0.07228915663x. Take half its coefficient (-0.03614457832). Square it (0.001306430542) and add it to both sides. Add '0.001306430542' to each side of the equation. -0.07228915663x + 0.001306430542 + x2 = -1.084337349 + 0.001306430542 Reorder the terms: 0.001306430542 + -0.07228915663x + x2 = -1.084337349 + 0.001306430542 Combine like terms: -1.084337349 + 0.001306430542 = -1.083030918458 0.001306430542 + -0.07228915663x + x2 = -1.083030918458 Factor a perfect square on the left side: (x + -0.03614457832)(x + -0.03614457832) = -1.083030918458 Can't calculate square root of the right side. The solution to this equation could not be determined.
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