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Simplifying 0.0012x2 + 1.0591x + -120.909 = 0 Reorder the terms: -120.909 + 1.0591x + 0.0012x2 = 0 Solving -120.909 + 1.0591x + 0.0012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0012 the coefficient of the squared term: Divide each side by '0.0012'. -100757.5 + 882.5833333x + x2 = 0 Move the constant term to the right: Add '100757.5' to each side of the equation. -100757.5 + 882.5833333x + 100757.5 + x2 = 0 + 100757.5 Reorder the terms: -100757.5 + 100757.5 + 882.5833333x + x2 = 0 + 100757.5 Combine like terms: -100757.5 + 100757.5 = 0.0 0.0 + 882.5833333x + x2 = 0 + 100757.5 882.5833333x + x2 = 0 + 100757.5 Combine like terms: 0 + 100757.5 = 100757.5 882.5833333x + x2 = 100757.5 The x term is 882.5833333x. Take half its coefficient (441.2916667). Square it (194738.3351) and add it to both sides. Add '194738.3351' to each side of the equation. 882.5833333x + 194738.3351 + x2 = 100757.5 + 194738.3351 Reorder the terms: 194738.3351 + 882.5833333x + x2 = 100757.5 + 194738.3351 Combine like terms: 100757.5 + 194738.3351 = 295495.8351 194738.3351 + 882.5833333x + x2 = 295495.8351 Factor a perfect square on the left side: (x + 441.2916667)(x + 441.2916667) = 295495.8351 Calculate the square root of the right side: 543.595286127 Break this problem into two subproblems by setting (x + 441.2916667) equal to 543.595286127 and -543.595286127.Subproblem 1
x + 441.2916667 = 543.595286127 Simplifying x + 441.2916667 = 543.595286127 Reorder the terms: 441.2916667 + x = 543.595286127 Solving 441.2916667 + x = 543.595286127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-441.2916667' to each side of the equation. 441.2916667 + -441.2916667 + x = 543.595286127 + -441.2916667 Combine like terms: 441.2916667 + -441.2916667 = 0.0000000 0.0000000 + x = 543.595286127 + -441.2916667 x = 543.595286127 + -441.2916667 Combine like terms: 543.595286127 + -441.2916667 = 102.303619427 x = 102.303619427 Simplifying x = 102.303619427Subproblem 2
x + 441.2916667 = -543.595286127 Simplifying x + 441.2916667 = -543.595286127 Reorder the terms: 441.2916667 + x = -543.595286127 Solving 441.2916667 + x = -543.595286127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-441.2916667' to each side of the equation. 441.2916667 + -441.2916667 + x = -543.595286127 + -441.2916667 Combine like terms: 441.2916667 + -441.2916667 = 0.0000000 0.0000000 + x = -543.595286127 + -441.2916667 x = -543.595286127 + -441.2916667 Combine like terms: -543.595286127 + -441.2916667 = -984.886952827 x = -984.886952827 Simplifying x = -984.886952827Solution
The solution to the problem is based on the solutions from the subproblems. x = {102.303619427, -984.886952827}
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