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Simplifying 0.0795(x2) + -0.9060(x) + 1.825 = 0 Reorder the terms: 1.825 + -0.9060x + 0.0795x2 = 0 Solving 1.825 + -0.9060x + 0.0795x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 22.95597484 + -11.39622642x + x2 = 0 Move the constant term to the right: Add '-22.95597484' to each side of the equation. 22.95597484 + -11.39622642x + -22.95597484 + x2 = 0 + -22.95597484 Reorder the terms: 22.95597484 + -22.95597484 + -11.39622642x + x2 = 0 + -22.95597484 Combine like terms: 22.95597484 + -22.95597484 = 0.00000000 0.00000000 + -11.39622642x + x2 = 0 + -22.95597484 -11.39622642x + x2 = 0 + -22.95597484 Combine like terms: 0 + -22.95597484 = -22.95597484 -11.39622642x + x2 = -22.95597484 The x term is -11.39622642x. Take half its coefficient (-5.69811321). Square it (32.46849415) and add it to both sides. Add '32.46849415' to each side of the equation. -11.39622642x + 32.46849415 + x2 = -22.95597484 + 32.46849415 Reorder the terms: 32.46849415 + -11.39622642x + x2 = -22.95597484 + 32.46849415 Combine like terms: -22.95597484 + 32.46849415 = 9.51251931 32.46849415 + -11.39622642x + x2 = 9.51251931 Factor a perfect square on the left side: (x + -5.69811321)(x + -5.69811321) = 9.51251931 Calculate the square root of the right side: 3.084237233 Break this problem into two subproblems by setting (x + -5.69811321) equal to 3.084237233 and -3.084237233.Subproblem 1
x + -5.69811321 = 3.084237233 Simplifying x + -5.69811321 = 3.084237233 Reorder the terms: -5.69811321 + x = 3.084237233 Solving -5.69811321 + x = 3.084237233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.69811321' to each side of the equation. -5.69811321 + 5.69811321 + x = 3.084237233 + 5.69811321 Combine like terms: -5.69811321 + 5.69811321 = 0.00000000 0.00000000 + x = 3.084237233 + 5.69811321 x = 3.084237233 + 5.69811321 Combine like terms: 3.084237233 + 5.69811321 = 8.782350443 x = 8.782350443 Simplifying x = 8.782350443Subproblem 2
x + -5.69811321 = -3.084237233 Simplifying x + -5.69811321 = -3.084237233 Reorder the terms: -5.69811321 + x = -3.084237233 Solving -5.69811321 + x = -3.084237233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.69811321' to each side of the equation. -5.69811321 + 5.69811321 + x = -3.084237233 + 5.69811321 Combine like terms: -5.69811321 + 5.69811321 = 0.00000000 0.00000000 + x = -3.084237233 + 5.69811321 x = -3.084237233 + 5.69811321 Combine like terms: -3.084237233 + 5.69811321 = 2.613875977 x = 2.613875977 Simplifying x = 2.613875977Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.782350443, 2.613875977}
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