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Simplifying 7x2 = 9 + -5x Solving 7x2 = 9 + -5x Solving for variable 'x'. Reorder the terms: -9 + 5x + 7x2 = 9 + -5x + -9 + 5x Reorder the terms: -9 + 5x + 7x2 = 9 + -9 + -5x + 5x Combine like terms: 9 + -9 = 0 -9 + 5x + 7x2 = 0 + -5x + 5x -9 + 5x + 7x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -9 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 0.7142857143x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 0.7142857143x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 0.7142857143x + x2 = 0 + 1.285714286 0.7142857143x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 0.7142857143x + x2 = 1.285714286 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 1.285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 1.285714286 + 0.1275510204 Combine like terms: 1.285714286 + 0.1275510204 = 1.4132653064 0.1275510204 + 0.7142857143x + x2 = 1.4132653064 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 1.4132653064 Calculate the square root of the right side: 1.188808356 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 1.188808356 and -1.188808356.Subproblem 1
x + 0.3571428572 = 1.188808356 Simplifying x + 0.3571428572 = 1.188808356 Reorder the terms: 0.3571428572 + x = 1.188808356 Solving 0.3571428572 + x = 1.188808356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.188808356 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.188808356 + -0.3571428572 x = 1.188808356 + -0.3571428572 Combine like terms: 1.188808356 + -0.3571428572 = 0.8316654988 x = 0.8316654988 Simplifying x = 0.8316654988Subproblem 2
x + 0.3571428572 = -1.188808356 Simplifying x + 0.3571428572 = -1.188808356 Reorder the terms: 0.3571428572 + x = -1.188808356 Solving 0.3571428572 + x = -1.188808356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.188808356 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.188808356 + -0.3571428572 x = -1.188808356 + -0.3571428572 Combine like terms: -1.188808356 + -0.3571428572 = -1.5459512132 x = -1.5459512132 Simplifying x = -1.5459512132Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8316654988, -1.5459512132}
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