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Simplifying 3.5x2 + -14x + -40 = 0 Reorder the terms: -40 + -14x + 3.5x2 = 0 Solving -40 + -14x + 3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -11.42857143 + -4x + x2 = 0 Move the constant term to the right: Add '11.42857143' to each side of the equation. -11.42857143 + -4x + 11.42857143 + x2 = 0 + 11.42857143 Reorder the terms: -11.42857143 + 11.42857143 + -4x + x2 = 0 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + -4x + x2 = 0 + 11.42857143 -4x + x2 = 0 + 11.42857143 Combine like terms: 0 + 11.42857143 = 11.42857143 -4x + x2 = 11.42857143 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 11.42857143 + 4 Reorder the terms: 4 + -4x + x2 = 11.42857143 + 4 Combine like terms: 11.42857143 + 4 = 15.42857143 4 + -4x + x2 = 15.42857143 Factor a perfect square on the left side: (x + -2)(x + -2) = 15.42857143 Calculate the square root of the right side: 3.927922024 Break this problem into two subproblems by setting (x + -2) equal to 3.927922024 and -3.927922024.Subproblem 1
x + -2 = 3.927922024 Simplifying x + -2 = 3.927922024 Reorder the terms: -2 + x = 3.927922024 Solving -2 + x = 3.927922024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.927922024 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.927922024 + 2 x = 3.927922024 + 2 Combine like terms: 3.927922024 + 2 = 5.927922024 x = 5.927922024 Simplifying x = 5.927922024Subproblem 2
x + -2 = -3.927922024 Simplifying x + -2 = -3.927922024 Reorder the terms: -2 + x = -3.927922024 Solving -2 + x = -3.927922024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.927922024 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.927922024 + 2 x = -3.927922024 + 2 Combine like terms: -3.927922024 + 2 = -1.927922024 x = -1.927922024 Simplifying x = -1.927922024Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.927922024, -1.927922024}
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