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Simplifying 5x + 7x2 = 83 Solving 5x + 7x2 = 83 Solving for variable 'x'. Reorder the terms: -83 + 5x + 7x2 = 83 + -83 Combine like terms: 83 + -83 = 0 -83 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -11.85714286 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '11.85714286' to each side of the equation. -11.85714286 + 0.7142857143x + 11.85714286 + x2 = 0 + 11.85714286 Reorder the terms: -11.85714286 + 11.85714286 + 0.7142857143x + x2 = 0 + 11.85714286 Combine like terms: -11.85714286 + 11.85714286 = 0.00000000 0.00000000 + 0.7142857143x + x2 = 0 + 11.85714286 0.7142857143x + x2 = 0 + 11.85714286 Combine like terms: 0 + 11.85714286 = 11.85714286 0.7142857143x + x2 = 11.85714286 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 = 11.85714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 11.85714286 + 0.1275510204 Combine like terms: 11.85714286 + 0.1275510204 = 11.9846938804 0.1275510204 + 0.7142857143x + x2 = 11.9846938804 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 11.9846938804 Calculate the square root of the right side: 3.461891662 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 3.461891662 and -3.461891662.Subproblem 1
x + 0.3571428572 = 3.461891662 Simplifying x + 0.3571428572 = 3.461891662 Reorder the terms: 0.3571428572 + x = 3.461891662 Solving 0.3571428572 + x = 3.461891662 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 = 3.461891662 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 3.461891662 + -0.3571428572 x = 3.461891662 + -0.3571428572 Combine like terms: 3.461891662 + -0.3571428572 = 3.1047488048 x = 3.1047488048 Simplifying x = 3.1047488048Subproblem 2
x + 0.3571428572 = -3.461891662 Simplifying x + 0.3571428572 = -3.461891662 Reorder the terms: 0.3571428572 + x = -3.461891662 Solving 0.3571428572 + x = -3.461891662 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 = -3.461891662 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -3.461891662 + -0.3571428572 x = -3.461891662 + -0.3571428572 Combine like terms: -3.461891662 + -0.3571428572 = -3.8190345192 x = -3.8190345192 Simplifying x = -3.8190345192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1047488048, -3.8190345192}
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