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Simplifying (7x2 + -5x + -14) + (7x2 + 8x) = 0 Reorder the terms: (-14 + -5x + 7x2) + (7x2 + 8x) = 0 Remove parenthesis around (-14 + -5x + 7x2) -14 + -5x + 7x2 + (7x2 + 8x) = 0 Reorder the terms: -14 + -5x + 7x2 + (8x + 7x2) = 0 Remove parenthesis around (8x + 7x2) -14 + -5x + 7x2 + 8x + 7x2 = 0 Reorder the terms: -14 + -5x + 8x + 7x2 + 7x2 = 0 Combine like terms: -5x + 8x = 3x -14 + 3x + 7x2 + 7x2 = 0 Combine like terms: 7x2 + 7x2 = 14x2 -14 + 3x + 14x2 = 0 Solving -14 + 3x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1 + 0.2142857143x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.2142857143x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.2142857143x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.2142857143x + x2 = 0 + 1 0.2142857143x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.2142857143x + x2 = 1 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 = 1 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143x + x2 = 1 + 0.01147959185 Combine like terms: 1 + 0.01147959185 = 1.01147959185 0.01147959185 + 0.2142857143x + x2 = 1.01147959185 Factor a perfect square on the left side: (x + 0.1071428572)(x + 0.1071428572) = 1.01147959185 Calculate the square root of the right side: 1.005723417 Break this problem into two subproblems by setting (x + 0.1071428572) equal to 1.005723417 and -1.005723417.Subproblem 1
x + 0.1071428572 = 1.005723417 Simplifying x + 0.1071428572 = 1.005723417 Reorder the terms: 0.1071428572 + x = 1.005723417 Solving 0.1071428572 + x = 1.005723417 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 = 1.005723417 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x = 1.005723417 + -0.1071428572 x = 1.005723417 + -0.1071428572 Combine like terms: 1.005723417 + -0.1071428572 = 0.8985805598 x = 0.8985805598 Simplifying x = 0.8985805598Subproblem 2
x + 0.1071428572 = -1.005723417 Simplifying x + 0.1071428572 = -1.005723417 Reorder the terms: 0.1071428572 + x = -1.005723417 Solving 0.1071428572 + x = -1.005723417 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 = -1.005723417 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x = -1.005723417 + -0.1071428572 x = -1.005723417 + -0.1071428572 Combine like terms: -1.005723417 + -0.1071428572 = -1.1128662742 x = -1.1128662742 Simplifying x = -1.1128662742Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8985805598, -1.1128662742}
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