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Simplifying 14x2 + -3x + 7 = 10 Reorder the terms: 7 + -3x + 14x2 = 10 Solving 7 + -3x + 14x2 = 10 Solving for variable 'x'. Reorder the terms: 7 + -10 + -3x + 14x2 = 10 + -10 Combine like terms: 7 + -10 = -3 -3 + -3x + 14x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -3 + -3x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + -0.2142857143x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -0.2142857143x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -0.2142857143x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -0.2142857143x + x2 = 0 + 0.2142857143 -0.2142857143x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -0.2142857143x + x2 = 0.2142857143 The x term is -0.2142857143x. Take half its coefficient (-0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. -0.2142857143x + 0.01147959185 + x2 = 0.2142857143 + 0.01147959185 Reorder the terms: 0.01147959185 + -0.2142857143x + x2 = 0.2142857143 + 0.01147959185 Combine like terms: 0.2142857143 + 0.01147959185 = 0.22576530615 0.01147959185 + -0.2142857143x + x2 = 0.22576530615 Factor a perfect square on the left side: (x + -0.1071428572)(x + -0.1071428572) = 0.22576530615 Calculate the square root of the right side: 0.475147668 Break this problem into two subproblems by setting (x + -0.1071428572) equal to 0.475147668 and -0.475147668.Subproblem 1
x + -0.1071428572 = 0.475147668 Simplifying x + -0.1071428572 = 0.475147668 Reorder the terms: -0.1071428572 + x = 0.475147668 Solving -0.1071428572 + x = 0.475147668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1071428572' to each side of the equation. -0.1071428572 + 0.1071428572 + x = 0.475147668 + 0.1071428572 Combine like terms: -0.1071428572 + 0.1071428572 = 0.0000000000 0.0000000000 + x = 0.475147668 + 0.1071428572 x = 0.475147668 + 0.1071428572 Combine like terms: 0.475147668 + 0.1071428572 = 0.5822905252 x = 0.5822905252 Simplifying x = 0.5822905252Subproblem 2
x + -0.1071428572 = -0.475147668 Simplifying x + -0.1071428572 = -0.475147668 Reorder the terms: -0.1071428572 + x = -0.475147668 Solving -0.1071428572 + x = -0.475147668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1071428572' to each side of the equation. -0.1071428572 + 0.1071428572 + x = -0.475147668 + 0.1071428572 Combine like terms: -0.1071428572 + 0.1071428572 = 0.0000000000 0.0000000000 + x = -0.475147668 + 0.1071428572 x = -0.475147668 + 0.1071428572 Combine like terms: -0.475147668 + 0.1071428572 = -0.3680048108 x = -0.3680048108 Simplifying x = -0.3680048108Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5822905252, -0.3680048108}
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