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Simplifying 7x2 = -10x + 3 Reorder the terms: 7x2 = 3 + -10x Solving 7x2 = 3 + -10x Solving for variable 'x'. Reorder the terms: -3 + 10x + 7x2 = 3 + -10x + -3 + 10x Reorder the terms: -3 + 10x + 7x2 = 3 + -3 + -10x + 10x Combine like terms: 3 + -3 = 0 -3 + 10x + 7x2 = 0 + -10x + 10x -3 + 10x + 7x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -3 + 10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.428571429x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.428571429x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + 0.4285714286 1.428571429x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.428571429x + x2 = 0.4285714286 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 = 0.4285714286 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 0.4285714286 + 0.5102040819 Combine like terms: 0.4285714286 + 0.5102040819 = 0.9387755105 0.5102040819 + 1.428571429x + x2 = 0.9387755105 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 0.9387755105 Calculate the square root of the right side: 0.968904283 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 0.968904283 and -0.968904283.Subproblem 1
x + 0.7142857145 = 0.968904283 Simplifying x + 0.7142857145 = 0.968904283 Reorder the terms: 0.7142857145 + x = 0.968904283 Solving 0.7142857145 + x = 0.968904283 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 = 0.968904283 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.968904283 + -0.7142857145 x = 0.968904283 + -0.7142857145 Combine like terms: 0.968904283 + -0.7142857145 = 0.2546185685 x = 0.2546185685 Simplifying x = 0.2546185685Subproblem 2
x + 0.7142857145 = -0.968904283 Simplifying x + 0.7142857145 = -0.968904283 Reorder the terms: 0.7142857145 + x = -0.968904283 Solving 0.7142857145 + x = -0.968904283 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 = -0.968904283 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.968904283 + -0.7142857145 x = -0.968904283 + -0.7142857145 Combine like terms: -0.968904283 + -0.7142857145 = -1.6831899975 x = -1.6831899975 Simplifying x = -1.6831899975Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2546185685, -1.6831899975}
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