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Simplifying 98x2 + 53x + 6 = 0 Reorder the terms: 6 + 53x + 98x2 = 0 Solving 6 + 53x + 98x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. 0.0612244898 + 0.5408163265x + x2 = 0 Move the constant term to the right: Add '-0.0612244898' to each side of the equation. 0.0612244898 + 0.5408163265x + -0.0612244898 + x2 = 0 + -0.0612244898 Reorder the terms: 0.0612244898 + -0.0612244898 + 0.5408163265x + x2 = 0 + -0.0612244898 Combine like terms: 0.0612244898 + -0.0612244898 = 0.0000000000 0.0000000000 + 0.5408163265x + x2 = 0 + -0.0612244898 0.5408163265x + x2 = 0 + -0.0612244898 Combine like terms: 0 + -0.0612244898 = -0.0612244898 0.5408163265x + x2 = -0.0612244898 The x term is 0.5408163265x. Take half its coefficient (0.2704081633). Square it (0.07312057478) and add it to both sides. Add '0.07312057478' to each side of the equation. 0.5408163265x + 0.07312057478 + x2 = -0.0612244898 + 0.07312057478 Reorder the terms: 0.07312057478 + 0.5408163265x + x2 = -0.0612244898 + 0.07312057478 Combine like terms: -0.0612244898 + 0.07312057478 = 0.01189608498 0.07312057478 + 0.5408163265x + x2 = 0.01189608498 Factor a perfect square on the left side: (x + 0.2704081633)(x + 0.2704081633) = 0.01189608498 Calculate the square root of the right side: 0.109069175 Break this problem into two subproblems by setting (x + 0.2704081633) equal to 0.109069175 and -0.109069175.Subproblem 1
x + 0.2704081633 = 0.109069175 Simplifying x + 0.2704081633 = 0.109069175 Reorder the terms: 0.2704081633 + x = 0.109069175 Solving 0.2704081633 + x = 0.109069175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2704081633' to each side of the equation. 0.2704081633 + -0.2704081633 + x = 0.109069175 + -0.2704081633 Combine like terms: 0.2704081633 + -0.2704081633 = 0.0000000000 0.0000000000 + x = 0.109069175 + -0.2704081633 x = 0.109069175 + -0.2704081633 Combine like terms: 0.109069175 + -0.2704081633 = -0.1613389883 x = -0.1613389883 Simplifying x = -0.1613389883Subproblem 2
x + 0.2704081633 = -0.109069175 Simplifying x + 0.2704081633 = -0.109069175 Reorder the terms: 0.2704081633 + x = -0.109069175 Solving 0.2704081633 + x = -0.109069175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2704081633' to each side of the equation. 0.2704081633 + -0.2704081633 + x = -0.109069175 + -0.2704081633 Combine like terms: 0.2704081633 + -0.2704081633 = 0.0000000000 0.0000000000 + x = -0.109069175 + -0.2704081633 x = -0.109069175 + -0.2704081633 Combine like terms: -0.109069175 + -0.2704081633 = -0.3794773383 x = -0.3794773383 Simplifying x = -0.3794773383Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1613389883, -0.3794773383}
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