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Simplifying 34x2 + 43x + -2 = 0 Reorder the terms: -2 + 43x + 34x2 = 0 Solving -2 + 43x + 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'. -0.05882352941 + 1.264705882x + x2 = 0 Move the constant term to the right: Add '0.05882352941' to each side of the equation. -0.05882352941 + 1.264705882x + 0.05882352941 + x2 = 0 + 0.05882352941 Reorder the terms: -0.05882352941 + 0.05882352941 + 1.264705882x + x2 = 0 + 0.05882352941 Combine like terms: -0.05882352941 + 0.05882352941 = 0.00000000000 0.00000000000 + 1.264705882x + x2 = 0 + 0.05882352941 1.264705882x + x2 = 0 + 0.05882352941 Combine like terms: 0 + 0.05882352941 = 0.05882352941 1.264705882x + x2 = 0.05882352941 The x term is 1.264705882x. Take half its coefficient (0.632352941). Square it (0.3998702420) and add it to both sides. Add '0.3998702420' to each side of the equation. 1.264705882x + 0.3998702420 + x2 = 0.05882352941 + 0.3998702420 Reorder the terms: 0.3998702420 + 1.264705882x + x2 = 0.05882352941 + 0.3998702420 Combine like terms: 0.05882352941 + 0.3998702420 = 0.45869377141 0.3998702420 + 1.264705882x + x2 = 0.45869377141 Factor a perfect square on the left side: (x + 0.632352941)(x + 0.632352941) = 0.45869377141 Calculate the square root of the right side: 0.677269349 Break this problem into two subproblems by setting (x + 0.632352941) equal to 0.677269349 and -0.677269349.Subproblem 1
x + 0.632352941 = 0.677269349 Simplifying x + 0.632352941 = 0.677269349 Reorder the terms: 0.632352941 + x = 0.677269349 Solving 0.632352941 + x = 0.677269349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.632352941' to each side of the equation. 0.632352941 + -0.632352941 + x = 0.677269349 + -0.632352941 Combine like terms: 0.632352941 + -0.632352941 = 0.000000000 0.000000000 + x = 0.677269349 + -0.632352941 x = 0.677269349 + -0.632352941 Combine like terms: 0.677269349 + -0.632352941 = 0.044916408 x = 0.044916408 Simplifying x = 0.044916408Subproblem 2
x + 0.632352941 = -0.677269349 Simplifying x + 0.632352941 = -0.677269349 Reorder the terms: 0.632352941 + x = -0.677269349 Solving 0.632352941 + x = -0.677269349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.632352941' to each side of the equation. 0.632352941 + -0.632352941 + x = -0.677269349 + -0.632352941 Combine like terms: 0.632352941 + -0.632352941 = 0.000000000 0.000000000 + x = -0.677269349 + -0.632352941 x = -0.677269349 + -0.632352941 Combine like terms: -0.677269349 + -0.632352941 = -1.30962229 x = -1.30962229 Simplifying x = -1.30962229Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.044916408, -1.30962229}
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