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Simplifying 121x2 + -532x + 282 = 0 Reorder the terms: 282 + -532x + 121x2 = 0 Solving 282 + -532x + 121x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. 2.330578512 + -4.396694215x + x2 = 0 Move the constant term to the right: Add '-2.330578512' to each side of the equation. 2.330578512 + -4.396694215x + -2.330578512 + x2 = 0 + -2.330578512 Reorder the terms: 2.330578512 + -2.330578512 + -4.396694215x + x2 = 0 + -2.330578512 Combine like terms: 2.330578512 + -2.330578512 = 0.000000000 0.000000000 + -4.396694215x + x2 = 0 + -2.330578512 -4.396694215x + x2 = 0 + -2.330578512 Combine like terms: 0 + -2.330578512 = -2.330578512 -4.396694215x + x2 = -2.330578512 The x term is -4.396694215x. Take half its coefficient (-2.198347108). Square it (4.832730007) and add it to both sides. Add '4.832730007' to each side of the equation. -4.396694215x + 4.832730007 + x2 = -2.330578512 + 4.832730007 Reorder the terms: 4.832730007 + -4.396694215x + x2 = -2.330578512 + 4.832730007 Combine like terms: -2.330578512 + 4.832730007 = 2.502151495 4.832730007 + -4.396694215x + x2 = 2.502151495 Factor a perfect square on the left side: (x + -2.198347108)(x + -2.198347108) = 2.502151495 Calculate the square root of the right side: 1.581819046 Break this problem into two subproblems by setting (x + -2.198347108) equal to 1.581819046 and -1.581819046.Subproblem 1
x + -2.198347108 = 1.581819046 Simplifying x + -2.198347108 = 1.581819046 Reorder the terms: -2.198347108 + x = 1.581819046 Solving -2.198347108 + x = 1.581819046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.198347108' to each side of the equation. -2.198347108 + 2.198347108 + x = 1.581819046 + 2.198347108 Combine like terms: -2.198347108 + 2.198347108 = 0.000000000 0.000000000 + x = 1.581819046 + 2.198347108 x = 1.581819046 + 2.198347108 Combine like terms: 1.581819046 + 2.198347108 = 3.780166154 x = 3.780166154 Simplifying x = 3.780166154Subproblem 2
x + -2.198347108 = -1.581819046 Simplifying x + -2.198347108 = -1.581819046 Reorder the terms: -2.198347108 + x = -1.581819046 Solving -2.198347108 + x = -1.581819046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.198347108' to each side of the equation. -2.198347108 + 2.198347108 + x = -1.581819046 + 2.198347108 Combine like terms: -2.198347108 + 2.198347108 = 0.000000000 0.000000000 + x = -1.581819046 + 2.198347108 x = -1.581819046 + 2.198347108 Combine like terms: -1.581819046 + 2.198347108 = 0.616528062 x = 0.616528062 Simplifying x = 0.616528062Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.780166154, 0.616528062}
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