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Simplifying 0.0031716 + -8.304x2 + -1x = 0 Reorder the terms: 0.0031716 + -1x + -8.304x2 = 0 Solving 0.0031716 + -1x + -8.304x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8.304 the coefficient of the squared term: Divide each side by '-8.304'. -0.0003819364162 + 0.1204238921x + x2 = 0 Move the constant term to the right: Add '0.0003819364162' to each side of the equation. -0.0003819364162 + 0.1204238921x + 0.0003819364162 + x2 = 0 + 0.0003819364162 Reorder the terms: -0.0003819364162 + 0.0003819364162 + 0.1204238921x + x2 = 0 + 0.0003819364162 Combine like terms: -0.0003819364162 + 0.0003819364162 = 0.0000000000000 0.0000000000000 + 0.1204238921x + x2 = 0 + 0.0003819364162 0.1204238921x + x2 = 0 + 0.0003819364162 Combine like terms: 0 + 0.0003819364162 = 0.0003819364162 0.1204238921x + x2 = 0.0003819364162 The x term is 0.1204238921x. Take half its coefficient (0.06021194605). Square it (0.003625478447) and add it to both sides. Add '0.003625478447' to each side of the equation. 0.1204238921x + 0.003625478447 + x2 = 0.0003819364162 + 0.003625478447 Reorder the terms: 0.003625478447 + 0.1204238921x + x2 = 0.0003819364162 + 0.003625478447 Combine like terms: 0.0003819364162 + 0.003625478447 = 0.0040074148632 0.003625478447 + 0.1204238921x + x2 = 0.0040074148632 Factor a perfect square on the left side: (x + 0.06021194605)(x + 0.06021194605) = 0.0040074148632 Calculate the square root of the right side: 0.063304146 Break this problem into two subproblems by setting (x + 0.06021194605) equal to 0.063304146 and -0.063304146.Subproblem 1
x + 0.06021194605 = 0.063304146 Simplifying x + 0.06021194605 = 0.063304146 Reorder the terms: 0.06021194605 + x = 0.063304146 Solving 0.06021194605 + x = 0.063304146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06021194605' to each side of the equation. 0.06021194605 + -0.06021194605 + x = 0.063304146 + -0.06021194605 Combine like terms: 0.06021194605 + -0.06021194605 = 0.00000000000 0.00000000000 + x = 0.063304146 + -0.06021194605 x = 0.063304146 + -0.06021194605 Combine like terms: 0.063304146 + -0.06021194605 = 0.00309219995 x = 0.00309219995 Simplifying x = 0.00309219995Subproblem 2
x + 0.06021194605 = -0.063304146 Simplifying x + 0.06021194605 = -0.063304146 Reorder the terms: 0.06021194605 + x = -0.063304146 Solving 0.06021194605 + x = -0.063304146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06021194605' to each side of the equation. 0.06021194605 + -0.06021194605 + x = -0.063304146 + -0.06021194605 Combine like terms: 0.06021194605 + -0.06021194605 = 0.00000000000 0.00000000000 + x = -0.063304146 + -0.06021194605 x = -0.063304146 + -0.06021194605 Combine like terms: -0.063304146 + -0.06021194605 = -0.12351609205 x = -0.12351609205 Simplifying x = -0.12351609205Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00309219995, -0.12351609205}
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