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Simplifying 0.024964x2 + -1.999192x + -0.001756 = 0 Reorder the terms: -0.001756 + -1.999192x + 0.024964x2 = 0 Solving -0.001756 + -1.999192x + 0.024964x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.024964 the coefficient of the squared term: Divide each side by '0.024964'. -0.07034129146 + -80.08299952x + x2 = 0 Move the constant term to the right: Add '0.07034129146' to each side of the equation. -0.07034129146 + -80.08299952x + 0.07034129146 + x2 = 0 + 0.07034129146 Reorder the terms: -0.07034129146 + 0.07034129146 + -80.08299952x + x2 = 0 + 0.07034129146 Combine like terms: -0.07034129146 + 0.07034129146 = 0.00000000000 0.00000000000 + -80.08299952x + x2 = 0 + 0.07034129146 -80.08299952x + x2 = 0 + 0.07034129146 Combine like terms: 0 + 0.07034129146 = 0.07034129146 -80.08299952x + x2 = 0.07034129146 The x term is -80.08299952x. Take half its coefficient (-40.04149976). Square it (1603.321703) and add it to both sides. Add '1603.321703' to each side of the equation. -80.08299952x + 1603.321703 + x2 = 0.07034129146 + 1603.321703 Reorder the terms: 1603.321703 + -80.08299952x + x2 = 0.07034129146 + 1603.321703 Combine like terms: 0.07034129146 + 1603.321703 = 1603.39204429146 1603.321703 + -80.08299952x + x2 = 1603.39204429146 Factor a perfect square on the left side: (x + -40.04149976)(x + -40.04149976) = 1603.39204429146 Calculate the square root of the right side: 40.042378105 Break this problem into two subproblems by setting (x + -40.04149976) equal to 40.042378105 and -40.042378105.Subproblem 1
x + -40.04149976 = 40.042378105 Simplifying x + -40.04149976 = 40.042378105 Reorder the terms: -40.04149976 + x = 40.042378105 Solving -40.04149976 + x = 40.042378105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.04149976' to each side of the equation. -40.04149976 + 40.04149976 + x = 40.042378105 + 40.04149976 Combine like terms: -40.04149976 + 40.04149976 = 0.00000000 0.00000000 + x = 40.042378105 + 40.04149976 x = 40.042378105 + 40.04149976 Combine like terms: 40.042378105 + 40.04149976 = 80.083877865 x = 80.083877865 Simplifying x = 80.083877865Subproblem 2
x + -40.04149976 = -40.042378105 Simplifying x + -40.04149976 = -40.042378105 Reorder the terms: -40.04149976 + x = -40.042378105 Solving -40.04149976 + x = -40.042378105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.04149976' to each side of the equation. -40.04149976 + 40.04149976 + x = -40.042378105 + 40.04149976 Combine like terms: -40.04149976 + 40.04149976 = 0.00000000 0.00000000 + x = -40.042378105 + 40.04149976 x = -40.042378105 + 40.04149976 Combine like terms: -40.042378105 + 40.04149976 = -0.000878345 x = -0.000878345 Simplifying x = -0.000878345Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.083877865, -0.000878345}
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