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Simplifying 1.4x2 + -2x + -10 = 0 Reorder the terms: -10 + -2x + 1.4x2 = 0 Solving -10 + -2x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -7.142857143 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + -1.428571429x + 7.142857143 + x2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + -1.428571429x + x2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + 7.142857143 -1.428571429x + x2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 -1.428571429x + x2 = 7.142857143 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 7.142857143 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 7.142857143 + 0.5102040819 Combine like terms: 7.142857143 + 0.5102040819 = 7.6530612249 0.5102040819 + -1.428571429x + x2 = 7.6530612249 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 7.6530612249 Calculate the square root of the right side: 2.766416676 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 2.766416676 and -2.766416676.Subproblem 1
x + -0.7142857145 = 2.766416676 Simplifying x + -0.7142857145 = 2.766416676 Reorder the terms: -0.7142857145 + x = 2.766416676 Solving -0.7142857145 + x = 2.766416676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 2.766416676 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 2.766416676 + 0.7142857145 x = 2.766416676 + 0.7142857145 Combine like terms: 2.766416676 + 0.7142857145 = 3.4807023905 x = 3.4807023905 Simplifying x = 3.4807023905Subproblem 2
x + -0.7142857145 = -2.766416676 Simplifying x + -0.7142857145 = -2.766416676 Reorder the terms: -0.7142857145 + x = -2.766416676 Solving -0.7142857145 + x = -2.766416676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -2.766416676 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -2.766416676 + 0.7142857145 x = -2.766416676 + 0.7142857145 Combine like terms: -2.766416676 + 0.7142857145 = -2.0521309615 x = -2.0521309615 Simplifying x = -2.0521309615Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4807023905, -2.0521309615}
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