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Simplifying 7x2 + 2 + 7x = -3x Reorder the terms: 2 + 7x + 7x2 = -3x Solving 2 + 7x + 7x2 = -3x Solving for variable 'x'. Reorder the terms: 2 + 7x + 3x + 7x2 = -3x + 3x Combine like terms: 7x + 3x = 10x 2 + 10x + 7x2 = -3x + 3x Combine like terms: -3x + 3x = 0 2 + 10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.428571429x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + -0.2857142857 1.428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.428571429x + x2 = -0.2857142857 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 = -0.2857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = -0.2857142857 + 0.5102040819 Combine like terms: -0.2857142857 + 0.5102040819 = 0.2244897962 0.5102040819 + 1.428571429x + x2 = 0.2244897962 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 0.2244897962 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 0.473803542 and -0.473803542.Subproblem 1
x + 0.7142857145 = 0.473803542 Simplifying x + 0.7142857145 = 0.473803542 Reorder the terms: 0.7142857145 + x = 0.473803542 Solving 0.7142857145 + x = 0.473803542 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 = 0.473803542 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.473803542 + -0.7142857145 x = 0.473803542 + -0.7142857145 Combine like terms: 0.473803542 + -0.7142857145 = -0.2404821725 x = -0.2404821725 Simplifying x = -0.2404821725Subproblem 2
x + 0.7142857145 = -0.473803542 Simplifying x + 0.7142857145 = -0.473803542 Reorder the terms: 0.7142857145 + x = -0.473803542 Solving 0.7142857145 + x = -0.473803542 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 = -0.473803542 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.473803542 + -0.7142857145 x = -0.473803542 + -0.7142857145 Combine like terms: -0.473803542 + -0.7142857145 = -1.1880892565 x = -1.1880892565 Simplifying x = -1.1880892565Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2404821725, -1.1880892565}
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