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Simplifying 38x2 + 13x + -6 = 0 Reorder the terms: -6 + 13x + 38x2 = 0 Solving -6 + 13x + 38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. -0.1578947368 + 0.3421052632x + x2 = 0 Move the constant term to the right: Add '0.1578947368' to each side of the equation. -0.1578947368 + 0.3421052632x + 0.1578947368 + x2 = 0 + 0.1578947368 Reorder the terms: -0.1578947368 + 0.1578947368 + 0.3421052632x + x2 = 0 + 0.1578947368 Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000 0.0000000000 + 0.3421052632x + x2 = 0 + 0.1578947368 0.3421052632x + x2 = 0 + 0.1578947368 Combine like terms: 0 + 0.1578947368 = 0.1578947368 0.3421052632x + x2 = 0.1578947368 The x term is 0.3421052632x. Take half its coefficient (0.1710526316). Square it (0.02925900278) and add it to both sides. Add '0.02925900278' to each side of the equation. 0.3421052632x + 0.02925900278 + x2 = 0.1578947368 + 0.02925900278 Reorder the terms: 0.02925900278 + 0.3421052632x + x2 = 0.1578947368 + 0.02925900278 Combine like terms: 0.1578947368 + 0.02925900278 = 0.18715373958 0.02925900278 + 0.3421052632x + x2 = 0.18715373958 Factor a perfect square on the left side: (x + 0.1710526316)(x + 0.1710526316) = 0.18715373958 Calculate the square root of the right side: 0.43261269 Break this problem into two subproblems by setting (x + 0.1710526316) equal to 0.43261269 and -0.43261269.Subproblem 1
x + 0.1710526316 = 0.43261269 Simplifying x + 0.1710526316 = 0.43261269 Reorder the terms: 0.1710526316 + x = 0.43261269 Solving 0.1710526316 + x = 0.43261269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1710526316' to each side of the equation. 0.1710526316 + -0.1710526316 + x = 0.43261269 + -0.1710526316 Combine like terms: 0.1710526316 + -0.1710526316 = 0.0000000000 0.0000000000 + x = 0.43261269 + -0.1710526316 x = 0.43261269 + -0.1710526316 Combine like terms: 0.43261269 + -0.1710526316 = 0.2615600584 x = 0.2615600584 Simplifying x = 0.2615600584Subproblem 2
x + 0.1710526316 = -0.43261269 Simplifying x + 0.1710526316 = -0.43261269 Reorder the terms: 0.1710526316 + x = -0.43261269 Solving 0.1710526316 + x = -0.43261269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1710526316' to each side of the equation. 0.1710526316 + -0.1710526316 + x = -0.43261269 + -0.1710526316 Combine like terms: 0.1710526316 + -0.1710526316 = 0.0000000000 0.0000000000 + x = -0.43261269 + -0.1710526316 x = -0.43261269 + -0.1710526316 Combine like terms: -0.43261269 + -0.1710526316 = -0.6036653216 x = -0.6036653216 Simplifying x = -0.6036653216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2615600584, -0.6036653216}
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