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Simplifying 20x2 + 62x + 23 = 0 Reorder the terms: 23 + 62x + 20x2 = 0 Solving 23 + 62x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.15 + 3.1x + x2 = 0 Move the constant term to the right: Add '-1.15' to each side of the equation. 1.15 + 3.1x + -1.15 + x2 = 0 + -1.15 Reorder the terms: 1.15 + -1.15 + 3.1x + x2 = 0 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + 3.1x + x2 = 0 + -1.15 3.1x + x2 = 0 + -1.15 Combine like terms: 0 + -1.15 = -1.15 3.1x + x2 = -1.15 The x term is 3.1x. Take half its coefficient (1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. 3.1x + 2.4025 + x2 = -1.15 + 2.4025 Reorder the terms: 2.4025 + 3.1x + x2 = -1.15 + 2.4025 Combine like terms: -1.15 + 2.4025 = 1.2525 2.4025 + 3.1x + x2 = 1.2525 Factor a perfect square on the left side: (x + 1.55)(x + 1.55) = 1.2525 Calculate the square root of the right side: 1.119151464 Break this problem into two subproblems by setting (x + 1.55) equal to 1.119151464 and -1.119151464.Subproblem 1
x + 1.55 = 1.119151464 Simplifying x + 1.55 = 1.119151464 Reorder the terms: 1.55 + x = 1.119151464 Solving 1.55 + x = 1.119151464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + x = 1.119151464 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = 1.119151464 + -1.55 x = 1.119151464 + -1.55 Combine like terms: 1.119151464 + -1.55 = -0.430848536 x = -0.430848536 Simplifying x = -0.430848536Subproblem 2
x + 1.55 = -1.119151464 Simplifying x + 1.55 = -1.119151464 Reorder the terms: 1.55 + x = -1.119151464 Solving 1.55 + x = -1.119151464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + x = -1.119151464 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = -1.119151464 + -1.55 x = -1.119151464 + -1.55 Combine like terms: -1.119151464 + -1.55 = -2.669151464 x = -2.669151464 Simplifying x = -2.669151464Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.430848536, -2.669151464}
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