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Simplifying 34x2 + 15x + -6 = 0 Reorder the terms: -6 + 15x + 34x2 = 0 Solving -6 + 15x + 34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.1764705882 + 0.4411764706x + x2 = 0 Move the constant term to the right: Add '0.1764705882' to each side of the equation. -0.1764705882 + 0.4411764706x + 0.1764705882 + x2 = 0 + 0.1764705882 Reorder the terms: -0.1764705882 + 0.1764705882 + 0.4411764706x + x2 = 0 + 0.1764705882 Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000 0.0000000000 + 0.4411764706x + x2 = 0 + 0.1764705882 0.4411764706x + x2 = 0 + 0.1764705882 Combine like terms: 0 + 0.1764705882 = 0.1764705882 0.4411764706x + x2 = 0.1764705882 The x term is 0.4411764706x. Take half its coefficient (0.2205882353). Square it (0.04865916955) and add it to both sides. Add '0.04865916955' to each side of the equation. 0.4411764706x + 0.04865916955 + x2 = 0.1764705882 + 0.04865916955 Reorder the terms: 0.04865916955 + 0.4411764706x + x2 = 0.1764705882 + 0.04865916955 Combine like terms: 0.1764705882 + 0.04865916955 = 0.22512975775 0.04865916955 + 0.4411764706x + x2 = 0.22512975775 Factor a perfect square on the left side: (x + 0.2205882353)(x + 0.2205882353) = 0.22512975775 Calculate the square root of the right side: 0.474478406 Break this problem into two subproblems by setting (x + 0.2205882353) equal to 0.474478406 and -0.474478406.Subproblem 1
x + 0.2205882353 = 0.474478406 Simplifying x + 0.2205882353 = 0.474478406 Reorder the terms: 0.2205882353 + x = 0.474478406 Solving 0.2205882353 + x = 0.474478406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2205882353' to each side of the equation. 0.2205882353 + -0.2205882353 + x = 0.474478406 + -0.2205882353 Combine like terms: 0.2205882353 + -0.2205882353 = 0.0000000000 0.0000000000 + x = 0.474478406 + -0.2205882353 x = 0.474478406 + -0.2205882353 Combine like terms: 0.474478406 + -0.2205882353 = 0.2538901707 x = 0.2538901707 Simplifying x = 0.2538901707Subproblem 2
x + 0.2205882353 = -0.474478406 Simplifying x + 0.2205882353 = -0.474478406 Reorder the terms: 0.2205882353 + x = -0.474478406 Solving 0.2205882353 + x = -0.474478406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2205882353' to each side of the equation. 0.2205882353 + -0.2205882353 + x = -0.474478406 + -0.2205882353 Combine like terms: 0.2205882353 + -0.2205882353 = 0.0000000000 0.0000000000 + x = -0.474478406 + -0.2205882353 x = -0.474478406 + -0.2205882353 Combine like terms: -0.474478406 + -0.2205882353 = -0.6950666413 x = -0.6950666413 Simplifying x = -0.6950666413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2538901707, -0.6950666413}
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