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Simplifying 4.5x2 + 2x + -13 = 0 Reorder the terms: -13 + 2x + 4.5x2 = 0 Solving -13 + 2x + 4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. -2.888888889 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '2.888888889' to each side of the equation. -2.888888889 + 0.4444444444x + 2.888888889 + x2 = 0 + 2.888888889 Reorder the terms: -2.888888889 + 2.888888889 + 0.4444444444x + x2 = 0 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 2.888888889 0.4444444444x + x2 = 0 + 2.888888889 Combine like terms: 0 + 2.888888889 = 2.888888889 0.4444444444x + x2 = 2.888888889 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 2.888888889 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 2.888888889 + 0.04938271604 Combine like terms: 2.888888889 + 0.04938271604 = 2.93827160504 0.04938271604 + 0.4444444444x + x2 = 2.93827160504 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 2.93827160504 Calculate the square root of the right side: 1.714138736 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 1.714138736 and -1.714138736.Subproblem 1
x + 0.2222222222 = 1.714138736 Simplifying x + 0.2222222222 = 1.714138736 Reorder the terms: 0.2222222222 + x = 1.714138736 Solving 0.2222222222 + x = 1.714138736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 1.714138736 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 1.714138736 + -0.2222222222 x = 1.714138736 + -0.2222222222 Combine like terms: 1.714138736 + -0.2222222222 = 1.4919165138 x = 1.4919165138 Simplifying x = 1.4919165138Subproblem 2
x + 0.2222222222 = -1.714138736 Simplifying x + 0.2222222222 = -1.714138736 Reorder the terms: 0.2222222222 + x = -1.714138736 Solving 0.2222222222 + x = -1.714138736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -1.714138736 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -1.714138736 + -0.2222222222 x = -1.714138736 + -0.2222222222 Combine like terms: -1.714138736 + -0.2222222222 = -1.9363609582 x = -1.9363609582 Simplifying x = -1.9363609582Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4919165138, -1.9363609582}
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